From the polymorph subschool:
You can only be affected by one polymorph spell at a time. If a new polymorph spell is cast on you (or you activate a polymorph effect, such as wild shape), you can decide whether or not to allow it to affect you, taking the place of the old spell. In addition, other spells that change your size have no effect on you while you are under the effects of a polymorph spell.
While the above rule is enough for your case, there is also a Paizo FAQ which says that size changes never stack, even for spells that lack a non-stacking clause:
As per the rules on size changes, size changes do not stack, so if you have multiple size changing effects (for instance an effect that increases your size by one step and another that increases your size by two steps), only the largest applies.
However, I can't actually find the "rules on size changes" that the FAQ refers to. So afaict, like many FAQ entries, this is an errata and not just a clarification of previously existing rules.
Make it a Downtime Activity
More on less on par with Crafting a Magic Item.
This is how I approach permanency in the Eberron game that I run, and my players have been happy with it so far.
The initial problem
Trying to directly port Permanency into 5E is a problem, since Permanency had an XP cost, and using XP is an optional rule in 5E.
D&D 5e's Adventurer's League has a precedent for charging Downtime as a 'toll on the character's soul.' (See Here, the section on Jenny Greenteeth)
For further precedent...making a magical effect permanent is essentially what you are doing while crafting a magic item. So making a spell Permanent is following the same sort of procedure as you'd use to craft an enchanted item with a persistent effect...but you're attaching it to a person or place instead.
For the downtime activity of making a spell Permanent, I basically follow the rules for crafting a magic item, starting on page 128 of the DMG, using the 'Power By Rarity' table on page 285 to determine the 'effective rarity' of the spell to be made permanent.
Because Permanent spells can be torn down with Dispel Magic, I treat them as 'consumable' items (half the cost and creation time of a 'normal' magic item of that power level). If you want Permanency to be harder...then treat them as normal cost for their rarity level. And if you want to cap which spells can be made permanent, bear in mind that 3.5e actually had a rather short list of spells that could be made Permanent.
By dint of flavor, I generally say that making a spell Permanent doesn't actually take the full duration of you working on it. I rule that some of that time (often about half) has to be spent recovering from the physical and spiritual exertion of what you just did.
Naturally, you have to know the spell in order to make it permanent, and every day you spend working on the permanency, you burn an appropriate level spell slot to cast that spell.
Additionally, you need to be somewhere while working on this where you can acquire all the extra spell components needed to stabilize the spell into a self-sustaining loop.
Finally, because of the delicate nature of permanency...you can't interrupt your work. If you're in the first half of the downtime and you skip a day...you get to start over. If you're in the second half of the downtime, you're operating at 3 levels of exhaustion and that day doesn't count towards your recovery time.
Whoever (or whatever) is the recipient of the Permanent Spell, must be present the entire time the spellcaster is working on making the spell permanent (so, the entire workday for the first half of the downtime). After that, they may wander off while the spellcaster recovers.
"Can a creature employ the spell permanency to make permanent the same spell more than once to increase that spell's benefit?"
Usually no. Most spells with ongoing effects don't combine with themselves for greater efficacy. Instead, a spell does what it says it does, and only does what it says it does. This idea is covered in greater detail on Combining Magical Effects.
For example, the resistance spell grants a creature +1 resistance bonus to its saving throws. A creature affected by a second resistance spell gains the same +1 resistance bonus to saving throws that the creature had already received from the first resistance spell. (However, the creature would use the longest duration among the resistance spells cast upon it.)
"What if the the spell's description does not disallow casting it on a creature multiple times to increase the benefit the spell provides?"
In a game that relies on exception-based design, things work according to the rules except when the rules say they don't. This means a spell needn't specifically disallow multiple castings providing an increased benefit. Instead, a spell must specifically allow it to be cast multiple times for increased effect! This, too, is covered by Combining Magical Effects.
There's some debate whether the same spell can affect the same subject multiple times if each spell has an entirely different effect each time (e.g. resist energy).
On the resistance spell
The resistance spell specifically won't stack with itself because it grants the subject a named bonus. For more information search the Glossary for the entries stacking and bonus.