Could you use the pool points to make it large thus gaining the stat increases then when you needed him smaller use alter self to make him a med and get an addition +2 str on top of the large he already possessed?
I think the question is "do the bonuses from Enlarge Person and Alter Self stack." The answer is no. Both spells provide size bonuses, and because they are bonuses of the same type, they do not stack. That's based just on RAW.
Furthermore, it's listed for both spells that multiple spells that alter size do not stack with one another. Instead, they replace one another.
No you can't make a large eidolon stronger with alter self.
A creature that is transformed by a polymorph spell has to first have it's stats adjusted acording to the table describing the polymorph subtype (Link to description of polymorph subtype).
A large creature that becomes medium with alter self would first take -4 to Strength, -2 to Constitution, and gain a +2 Dexterity before getting the +2 enhancement bonus to Strength that alter self provides.
So it would likely be overall, -2 Strength, +2 Dexterity, -2 Constitution.
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No you can't make a large eidolon stronger with alter self.
A creature that is transformed by a polymorph spell has to first have it's stats adjusted acording to the table describing the polymorph subtype (Link to description of polymorph subtype).
A large creature that becomes medium with alter self would first take -4 to Strength, -2 to Constitution, and gain a +2 Dexterity before getting the +2 enhancement bonus to Strength that alter self provides.
So it would likely be overall, -2 Strength, +2 Dexterity, -2 Constitution.
Thanks this answered my question.