Eidolon Appearance - When can I Change it?

[Dr. Cliché]

I'm basically just wondering if and when I can change my Eidolon's appearance?

(I'm thinking of cosmetic stuff here - rather than stuff based on Evolutions, like tentacles or an extra head).

For example, let's say my Eidolon is initially in the form of a Draconic/lizard creature. However, I decide that I'd prefer it to look more like an Owlbear (obviously augmented with all current Evolutions).

Am I allowed to make that change immediately?

If not, am I allowed to make that change when I summon it?

Or would I have to wait until I levelled up and do it at the same time as I swapped Evolutions around?

Or would I just not be able to change its non-Evolution appearance at all? Is it just fixed once I've decided on it?

[Noxangelo]

if its just cosmetic there shouldn't be any reason not to change it whenever. talk to your DM, maybe he'll let you research a ritual that doesn't cost anything but maybe takes 8 hour to perform.

[Dr. Cliché]

if its just cosmetic there shouldn't be any reason not to change it whenever. talk to your DM, maybe he'll let you research a ritual that doesn't cost anything but maybe takes 8 hour to perform.

The DM is playing completely by RAW so I'm looking to find whether or not the rules actually permit this.

[Jack_Simth]

The DM is playing completely by RAW
No such animal. The rules cannot (and do not) cover everything.

Explicitly:
Most of the evolutions are full of flexible fluff (e.g., "Improved Natural Armor (Ex)" says "An eidolon’s hide grows thick fur, rigid scales, or bony plates" - it's not required that you pick any specific one, and one must be picked, so you can pick when you pick the evolution) so you can do some serious revamping any time you can change those (on level up, or when you cast Transmorgify).

You can of course also use illusion magic - a Ring of Chameleon Power, a Hat of Disguise, cast Disguise Self (UMD a Page of Spell Knowledge), have the party Wizard cast Veil, whatever.

Or you can try your hand at spell research. As Noxangelo noted: It has no mechanical impact, so should be easy enough.

[False God]

As far as I am aware, there is no way to do that without being the Evolutionist Archetype.