Becoming a centaur? As a synthesis.

[arcanine]

Can a synthesis summoner take a base quadruped, the limbs trait and get arms on the eidolon.
When we fuse would I be able to wield a lance? And be considered mounted because I have 4 legs?

And while in this form can I have someone ride me as well?

[kestral287]

You can take limbs for arms as a quadruped.

You can wield a lance when fused.

You are not considered mounted. Centaurs have a special ability for that; a Synthesist does not.

[Samasboy1]

There is a Tauric base form now, from Cohorts and Companions.

This should qualify you for Natural Jouster, as "any tauric creature at GM's discretion." At your GM's discretion, of course.

Someone could probably ride you, with or without the Mount evolution, but that seems to open more some cans of rule worms.