There are not a lot of really explicit rules about this; most such spells were imagined as being performed totally outside of combat and without any need or desire to try to do other things at the same time.
One way you can almost-certainly act is with the schism power. That allows you to effectively take a second standard action each round, but that standard action must be “purely mental.” Because it is only a standard action, it probably cannot take over concentrating on casting a spell (unlike concentrating on maintaining a spell already cast, which it might be able to handle assuming such a “transfer” is possible at all). However, it could perform other purely-mental standard actions while you spend your actual turn concentrating.
Other actions that get around the action limits imposed by spending a full-round action concentrating are more dubious, however. Schism is special because it literally sets up a second mind to act with “complete autonomy” and therefore almost-certainly does not interfere with concentration. Anything else you do implies that you are paying at least some attention elsewhere, and not on your casting. It’s unclear under the rules if you can do that.
For example, Travel Devotion allows you to move as a swift action, so you could do that without interfering with the action required to concentrate, but it’s not clear if the actual act of moving is something you can do while devoting this level of concentration to something. There’s a pretty good case to be made for it, though, since concentrating on maintaining a spell—which takes a standard action—is something most agree you can do while moving, and it is not on the official list of distractions. Still, the very fact that it takes a full-round action may mean that this kind of concentration is harder than maintaining a spell.
Similarly, an animal companion can be guided with a free action. Many usages of the Ride skill are also free actions. And both of those can, at least in some cases, be done without speaking or using your hands, if those are tied up casting a spell (it is unclear in the rules whether or not somatic and verbal components go on for the entirety of the casting). But they still take mental effort to think about what you want to do and direct things—can you do that without losing concentration on the spell?
Anyway, one thing you almost-certainly cannot do is cast another spell, or otherwise engage in something else that requires concentration. Schism, again, is a way around that.