The "correct" answer is that your assumptions are invalid. In my experience, a defender needing to enforce her mark more than once per round suggests both an over-zealous defender and an under-protected party.

However, in practical terms, if you're even asking this question it means that the "correct" answer isn't particularly useful. A defender should, most of the time, try to occupy the "tender mercies" of two enemies. They can, given their defenses, survive two enemies attacking them. If your GM is undaunted by mark-punishment there are a number of options, taken from my memory of the art of defending. There are 5 excellent threads here.

To rephrase your question in the realm of the practical then, the question is not simply "how do I enforce marks more than once per round" but "how do I attract and maintain the attention of two monsters?"

This raises the question of "aggro" and "stickiness". Aggro is a measure of how much a monster is inclined to hurt you. Having a painful punishment is an excellent way of raising aggro. Having high defenses is an excellent way of lowering aggro, especially if you consider the relative defenses of the defender and the party. If the defender is a low-damage wall, most sane monsters will simply ignore the wall. Don't be a wall. It's boring. (I speak from bitter experience here).

Stickiness is, effectively, soft control which prevents monsters who would otherwise move away from ... moving away. The fighter has failed to draw enough aggro and now must remind the monster to respect her. Defenders... vary... in terms of effective stickiness. Forced movement combined with a terrain feature of a wall or difficult terrain is an excellent sticky-amplifier, as is causing creatures to fall prone.

Therefore, some notes on how to manage aggro and stickiness as each type of defender at each tier.

Battlemind

The battlemind functionally has two "tiers" which are "before lightning rush" and "after lightning rush."

Before lightning rush

From levels 1-6, the battlemind is a fairly normal defender. They have absolutely no "sticky" capabilities, allowing marked monsters the free run of the place. To counterbalance, they are also quite happy to follow monsters if they are foolish enough to shift. With the right power choices (if your GM likes provoking) they can also perform quite punishing OAs.

To engage two monsters, both intent on attacking more squishy members of your party, you'll want to rely on conductive defense and vicious cobra strike. Conductive defense is a punishment stacker, dealing out primary damage as punishment whenever the enemy hits an ally. If the GM really is suicidal, combine it with mark of storm and flail expertise. Then they're prone and next to you. In order to attack someone else, they will have to provoke an OA from you (assuming no allies are in melee with them.) CD allows you to "sticky" one enemy by knocking it prone next to you with pseudo-punishment and keep another enemy marked. Don't forget the augment 1 to really discourage shifting. If you focus on this, your second at-will should be twisted eye for its augment 1: allowing you to use it on OA. (Or be a half-elf with eldritch strike). If enemies routinely violate your mark, go with a two-handed weapon. Not only will this lower your AC, (making you a more attractive target) but the BFWeapon in your hands will make most sane creatures think twice about giving you a free swing with it that debuffs them further.

After level 7 and lightning rush, the ability as an interrupt to whack an enemy who's silly enough to attack an ally within 5 squares of you is quite sufficient. The kicker here is to have a lightning (flail) with flail expertise and mark of storm (or be a half-elf). Then you can (if it's a melee attack) slide the enemy away from the ally, negating the attack, or, if they're a ranged attacker, get an OA then your lightning rush in. This should generate quite sufficient aggro, not to mention the proning and sliding shenanigans.

Cavalier

This class presents a few problems, to be honest. The defender aura is excellent for multiple-enforcement, and absolutely pathetic for actually doing your job of getting 2 enemies to attack you. It does, however, auto-damage whenever an enemy shifts out of the aura or attacks someone else while within it, so it does its job. The damage, however, is not sufficiently significant to worry an enemy who is attracted by the squishies surrounding you.

Righteous shield is a good 1/enc "no really, pay attention" but can't carry sufficient weight on its own. Given that your enforcement is OA based instead of II, shifting after your enemies isn't enough to maintain stickiness. The reduced daily count also isn't particularly impressive for this task. If you find yourself being in a position where the rest of your party is too squishy and the DM isn't respecting your radiance, your only real bet is to be human and grab power of earth and bolstering strike. Or, going by the recommendations of the charop guide, grab virtuous strike for power of arcana (white lotus hinderance is actually exceptionally good for stickiness if you can get your opponent against a wall) or power of the sun, which, to be fair, both does more damage and makes your radiance hurt far more, increasing your aggro, rather than your sticky. In higher tiers, it's about the same problem, but your dailies can compensate fairly well.

Knight

See above. Recently a series of feats for knights enhancing their power strike power have come out. Given that a knight performs an MBA on aura violation and slows on hit (you have hold the line, right?) there's no real "problem" with enforcing your aura against as many enemies as you want to hug. If you find that despite your quite impressive attacking capabilities they still want to be friends with your allies, you can invest in a lightning flail, flail expertise, and mark of storm to prone them, both when you attack with your MBA and when you punish them. Beyond that, the flail strike which prones them causes them to provoke when they stand from prone is absolutely delicious. This class is perfectly suited to multi-"marking" and insuring that enemies stick around. The only caveat is to consider your AC carefully, as you need to strike a balance between not being dead and having enemies dismiss your MBA as "weak" (more fool they). There's no real tier change in tactics.

Fighter

The fighter faces some difficulties in multi-marking, as noted in your question. However, fighters are past masters of both sticky and aggro-generation techniques.

In order to adequately assess a fighter, we must look at them in low heroic, high heroic, and paragon.

In low heroic, the best resource is the "battle-fury stance" By upping damage and dropping AC, you make your mark punishment non-trivially painful and increase the enemy's desire to attack you. This, combined with deft hurler cleave or dual strike is more than sufficient to lock down two targets with sufficient threat generation. If one target decides to provoke your MBA is more than sufficiently painful to punish him for that decision. Another option is the spear benefit of weapon master's strike, which causes them to provoke while shifting. This excellent power means that you can, quite literally, stop shifts (due to combat superiority).

If both enemies decide to break away (repeatedly) your best bet is to use tide of iron to position them against a surface. This way, they cannot shift-charge without provoking. While you can't tide both of them, mark of storm and a pair of lightning weapons (yes, this is starting to cost) with dual strike is more than enough to see the positioning through.

In high heroic, the sliding can be improved with rushing cleats a bludgeon expertise. With a slide 3 (from mark of storm or tide of iron), you'll be able to position your enemies exactly where you want them. Come and Get it (level 7 encounter power) is also effective in this regard. You may also want to investigate "Binding Style" which flat-out immobilizes the second target of dual strike. In this vein, you may want to consider a "net multiclass" to slow targets of your net attacks. Since a net is an off-hand weapon, it is an absolutely fantastic control technique, especially when combined with a slide.

In paragon, the level 16 gladiator champion dispenses with trickery and simply makes you undeniably sticky: Enemies cannot shift away from you. Period. Kulkor Arms Master rewards you significantly for proning opponents (quite achievable in many ways) and is considered one of the cheesiest fighter PPs. Son of Mercy is a bit single-target for your requirements, but is a lovely complement to dual strike for both damange and control of the person you don't have cornered.

Paladin

Paladins get both divine challenge and divine sanction. While the amount of punishment isn't particularly impressive, they can challenge and sanction different people, and accomplish multiple punishment actions in a turn, no extra stuff (beyond an at-will that can sanction) necessary.

Swordmage

Swordmages are.. difficult defenders to play. Assuming you're in paragon and have double-marking, your main recourse here is to mark (of shielding) someone and then ignore them, focusing your attacks on a second enemy. While there are no penalties for that second enemy to shift-charge away, sliding and/or proning that second enemy is a good "second best"

Warden

Wardens are absolutely fantastic at sticky, having a number of daily forms that create difficult terrain around them, as well as powers that slow (and feats that up damage of powers that slow.) Multi-target sticky is more difficult, and mainly is a result of form of winter's herald and treacherous ice. At-will sticky is from slowing a target that isn't pinned against the wall. Wardens have excellent PP options for difficult terrain and forced movement, the level 16 forced movement and the daily 20 polymorph are exactly what's needed in this situation. You may want to invest in feats which up the penalty to attacks from your mark, as multi-marking is trivial. Don't forget to take sudden roots. Mark of warding is one of them, as is razorclaw mark (not the best choice of race, but... interesting from an RP point of view). With a -3 to attack rolls and the soft control of slowing, immobilizing, and/or forced movement, you should be able to keep two targets engaged without difficulty.

Yes...sort of. More at L1 than at other levels though.

For a brief look at this, let's look at the 4 basic L1 characters and see what their defined combat options are.

• Wizard: 3 L1 spells/day (they get the extra from an afternoon nap). 3-4 cantrips. Generally the wizard has the most combat options. They have more daily spells than the cleric and they have several offensive cantrips to choose from (firebolt and ray of frost are the two that come to mind, they have another). Their cantrips either do a good bit of damage or slow or push. This gives them good options in melee, at range and on the daily power front. Lots of options on their turn.

• Cleric: 2 L1 spells/day, 3-4 cantrips. The cleric only has 1 attack cantrip, but the current cleric is designed to be played by a dwarf, and they get a genuine melee option (with proper stat allocation, it's better than their cantrips at L1). This gives them a good number of options (several of their cantrips are cool utilities in combat too). So they have a good number of choices on their turn.

• Rogue: no spells, all powers phrased in the form of Melee Basic Attack, and their cool movement power doesn't kick in until L2. The L1 rogue's only way to reliably generate Sneak Attack is to actually get into melee and find a buddy to stand next to their target (The other way is to stay at range, and also find a buddy to stand next to their target). Otherwise the L1 rogue does spend half their turns hiding (which is sad). So yeah, limited options here in combat (L1 rogue out of combat is a skill monkey and that's cool). Most of the combat decision for the rogue are whether or not to eat an opportunity attack to go over to the fighter's target to deal Sneak Attack on it.

• Fighter: Even more boring than the rogue. He has two main choices: which target am I going to hit with my weapon, and is it time to burn my Second Wind. Granted, this makes the fighter the most self sufficient character, but it doesn't provide many interesting combat options. Similar to the rogue, the fighter's best option sometimes is to eat the Opportunity Attack and walk over to the rogue's target so he doesn't have to eat the OA himself.

So yeah, L1 is pretty boring for the Fighter and the Rogue. Here's the good news: L1 is designed to be very short. And L2 is where a ton of the good stuff is for the Fighter and the Rogue*. The Rogue gets their class defining power: Cunning Action. This lets them hide, move and attack all in one turn (or disengage, move and attack all in one). This is the power that makes the rogue tick in a lot of ways. For the Fighter, they get the power that lets them compete with the rogue in damage 1-20. Their Action Surge power gives them a second meaningful per rest choice in encounters: they get another action on their turn.

Neither of these choices really solves the "I attack the goblin with my sword until he's dead." However, in many ways, this isn't all that different from the level of choice an Essentials class character has on their turn in 4e (well, it's fewer options, but it's fairly close by L2 I think).

Ultimately, breaking the "I attack the goblin until he's dead" cycle is not something that 5e addresses very well. It's left to the players to "try something interesting" to get the upper hand, and this seems to be encouraged by the system. Like it or not, this is 5e's design paradigm for Basic D&D. With the PHB coming out next month, two new martial archetypes for the fighter, and two new sub classes for the rogue should provide them with additional options on their turn (Eldritch knight is a gish type with spells, and the Battle Master fighter uses combat expertise dice to do other stuff).

*I think there is a pretty good reason for this. I believe this is largely to limit the effectiveness of single level MC dips into fighter and rogue to get some of their strongest powers (they already get a lot at L1, the fighter alone gets a fighting style, weapon and armor profs, and Second Wind.).