A really strict DM could rule that a creature can only catch one magic weapon that possesses the magic weapon special ability returning (Dungeon Master's Guide 225) (+1 bonus; 0 lbs.). That is, because the second returning weapon wasn't caught as soon as the creature could've caught it (like the first returning weapon was), the second (and third and so on) returning weapon falls at the creature's feet. (This player would find such a ruling needlessly harsh.)

However, I think that many DMs would rule that a typical creature that possesses only two hands must—as its first actions on its turn—take two free actions to catch two magic weapons that possess the magic weapon special ability returning and that any uncaught returning weapons afterward fall to the ground. Further, I suspect that many DMs will rule that catching more than two returning weapons is impossible for the typical creature with—sadly—only two hands.

(Getting more hands, by the way, is far from impossible. At its most basic a creature can buy a spare hand (Magic Item Compendium 137) (12,000 gp; 5 lbs.). Even in the core rules, a creature can be the subject of the 4th-level Sor/Wiz spell polymorph [trans] (Player's Handbook 263) so as to become a giant octopus (Monster Manual 281)—although not amphibious (306), it still has a 20 ft. land speed!)

A player can make a case for the magic weapon special ability returning having greater functionality than a cursory reading may indicate or make a case for catching multiple objects in one hand—and I'll discuss those below—, but, really, I'd expect a DM to tell a player that if he wants his PC to make iterative attacks with what is, essentially, the same thrown weapon, then the player should look into his PC taking the prestige class bloodstorm blade (Tome of Battle 100–5), buying the magic item gloves of endless javelins (Magic Item Compendium 194) (7,000 gp; 0 lbs.), or using the 1st-level Sor/Wiz spell blood wind [evoc] (Spell Compendium 33–4) or the 3rd-level kineticist power telekinetic boomerang [psychokinesis] (Races of the Wild 176), or some further method that straight-up just isn't the apparently lackluster magic weapon special ability returning.

That said, the adventurer who's a thrown weapon specialist treads a particularly frustrating path: the fighting style is all three of ability score-, feat-, and cost-intensive. Instead of strictly adhering to the rules, a DM that makes a house rule like this one so as to just make the magic weapon special ability returning better solves a problem the game doesn't really have an answer for.

Closeup: The magic weapon special ability returning

It's possible to lawyer the magic weapon special ability returning. This reader suggests this only if at wit's end trying to make returning work. Keep in mind that the potential for friction is present if making this argument. However, also keep in mind that there should be some reason to get the magic weapon special ability returning instead of teleporting (XPH 167) (+1 bonus; 0 lbs.).

Anyway, the magic weapon special ability returning says

This special ability can only be placed on a weapon that can be thrown. A returning weapon flies through the air back to the creature that threw it. It returns to the thrower just before the creature’s next turn (and is therefore ready to use again in that turn).

Catching a returning weapon when it comes back is a free action. If the character can’t catch it, or if the character has moved since throwing it, the weapon drops to the ground in the square from which it was thrown.

First, this reader imagines the weapon special ability's author envisioned returning would be placed on spears and throwing axes, but, in fact, any melee weapon can be thrown, making, for example, sword-chucking (not that kind) a viable lifestyle choice.

Second—and more importantly for the question's purposes—, the returning description doesn't detail what circumstances forbid a creature from catching a returning weapon (except for the creature having moved, obviously). So while one reader may finish If the character can’t catch it with because the character's hands are full, another reader may finish it with because the character's dead, paralyzed, or now missing its arms. Using this latter, broader reading, the magic weapon special ability returning gains some much-needed oomph: instead of clattering noisily and uselessly to the ground if the returning weapon wasn't caught at the earliest opportunity, now the returning weapon essentially waits for the creature that threw it—that's not dead, paralyzed, or missing its arms, by the way—to catch it.

If the DM buys that second reading (not a sure thing by any means—beer may help), then it's matter of negotiating how patient a returning weapon is. This player would initially propose that the weapon waits forevermore to be caught by the conscious and mobile warrior who threw it: Seriously, the magic weapon special ability mentions no time limit, it's a pretty silly magic weapon special ability anyway, and even warriors who throw stuff should occasionally be allowed to have nice things, right? This DM, though, would counter by saying that 1 round is sufficient and that the player should be grateful that the DM's this liberal (and then he'd thank you for the beer).

(I should note that creatures in campaigns that I DM that throw weapons tend to rely on the aforementioned glove of endless javelins. That magic item is simply easier to manage than the headache-inducing magic weapon special ability returning.)

Sage Advice: Holding multiple objects in one hand

The Dragon #308 Wizards Workshop column "Sage Advice: Weapons, Feats, Items, and Spells: Official Answers" includes on page 108 this exchange:

Can you hold throwing weapons in your off hand so that you don’t have to use an action to draw them? If so, how many skiprocks (or daggers, shurikens, darts, bullets, and so on) can be held “drawn” in an off-hand by a Small or Medium size character?

Sure, you can hold a few throwing weapons in one hand so they’re ready to throw without a separate action to draw them. When holding multiple weapons in your hand (or a single weapon too large for you to wield in one hand) you can’t use the weapon to attack, nor can you do anything else with that hand.

Bullets are ammunition and don’t have to be drawn. The other weapons on your list are thrown weapons and have to be drawn (except that skiprocks can be used with a sling as ammunition). Refer to the table below.

\begin{array}{lcc|l} \text{} & \text{Number} & \text{Extra Shafted} & \text{} \\ \text{Weapon Size}^1 & \text{Held} & \text{Weapons}^2 & \text{3.5 Equivalent}^3 \\ \hline \text{one size larger} & 1 & — & \text{2-handed or bigger weapon} \\ \text{your size} & 1 & +2 & \text{1-handed or bigger weapon} \\ \text{one size smaller} & 2 & +2 & \text{light weapon} \\ \text{two or more sizes smaller} & 3 & +2 & \text{inappropriately little light weapon} \\ \hline \end{array}

¹ In relation to your size.
² Spears, javelins, darts, and other weapons with fairly skinny shafts, but not weapons with fairly thick hafts such as axes.
³ This RPG.SE user added this column based on the 3.5 revision.

To my knowledge this exchange was never revisited in another product. It also predates the 3.5 revision, making it subject to minor adjustments by the DM (see Why a Revision on DMG 4). However, extrapolating from this ruling may allow a creature to catch multiple returning weapons in one hand (as per the table), though those weapons couldn't subsequently be used with that hand. That is, a creature would have to switch a weapon caught from an overfull hand to an empty hand to use that weapon. And, much like it's a free action to switch between wielding a 1-handed weapon in one hand to wielding it in two hands, I think that a DM that allows this advice into his campaign at all would allow a creature to take a free action to transfer a weapon from an overfull hand to an empty one so that it could be thrown normally.

Note: Sheathing a weapon as a free action is the subject of this question.

Only if you are ruled as using an improvised version of a proficient weapon

The relevant piece of information, PHB p. 147:

Improvised Weapons

In many cases, an improvised weapon is similar to an actual weapon and can be treated as such. For example, a table leg is akin to a club. At the DM’s option, a character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus.

An object that bears no resemblance to a weapon deals 1d4 damage (the DM assigns a damage type appropriate to the object). If a character uses a ranged weapon to make a melee attack, or throws a melee weapon that does not have the thrown property, it also deals 1d4 damage. An improvised thrown weapon has a normal range of 20 feet and a long range of 60 feet.

If you use an object that's similar to a weapon as if it were that weapon, that assumes you're using the weapon it was intended, with all of the applicable damage types, proficiencies, and properties associated with it.

Alternatively, if you use an object that bears no resemblance to a weapon, the object can deal 1d4 damage and the Thrown property.

However, you cannot use an object that's similar to a weapon and use it as if it were that weapon, and still have the object be something that bears no resemblance to a weapon.

If you attempt to throw a weapon without the thrown feature, you are no longer using the weapon the way it was intended, and it has to be treated as a different weapon. If a different weapon is applicable, use the new weapon's properties and proficiencies. Otherwise, treat it as an Improvised Weapon, with the applicable properties and proficiency.

With this information, you effectively have two choices:

1. Have your DM treat the original weapon as a second, different weapon that has the Thrown feature. Example: treating a Halfling's War Hammer (no Thrown) as a Goliath's Light Hammer (with Thrown).

2. Make your attack as using an Improvised Weapon, dealing 1d4 damage and using the default thrown option of 20/60 range, and only adding proficiency if provided by another feature (as from Kensei or Tavern Brawler)