I have since been directed to a section in my airlines FOM, and they do allow outside flying.
Basically, a pilot does have to get outside flying approved by the company with respect to "non-competition issues". For example, outside pt 121/135 would not be approved, but "generally" part 91 flying for compensation would be approved. Another issue is that flying does count toward your max flight time numbers (month, year, etc.), so you do have to report your flight times to the company for recordkeeping.