collaboration with a professor from other school Is it acceptable/advisable to seek to collaborate with a former professor (e.g. from undergrad school) while doing research with ones adviser at grad school (the two schools being different)? Of course, under the assumption that a conflict of interest is avoided (the process being transparent with both professors in agreement with it, the narrow research subjects don't overlap, etc.).

The main benefit of this over-hour endeavor is co-authorship in published papers and an additional recommendation source, along with satisfying ones desire to work on that specific problem.
Do it. It can only be good for you. And it is generally acceptable.

Make sure that your supervisor knows what's going on and approves, though if you are using your own time, there should be no reason not to approve.