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.