I believe I read that a Summoner's Eidelon can benefit from Augmented Summoning.
How about a Synthesist's Eidelon Suit?
Augmented Summoned doesn't work on Eidelons?
It's my understanding that the feat Augment Summoning won't work with the class ability to summon an Eidolon, it's not a spell; but if you use the spell Summon Eidolon to bring it into existence it will get the boosted stats from the feat.
Edit, I forgot to add the following.
Quite how it applies to the Synthesist however is up to the GM I guess.
Actually, I reread the feat, and since it's an enhancement bonus, it probably doesn't matter once you're at a high enough level to boost your Con and/or strength w/gear.
So I guess it would work w/Summon Eidelon, but isn't a great use of 2 feats for a relatively feat-starved class.