As Intruder says, the short answer is yes.
The long answer is, it depends. Most air operators will prohibit their employees from working for a competing company and would require their pilots to obtain permission before going to work for a non-competing company. When approval is given, it comes with some strict rules - at least at my outfit. Also, at least here in Canada, the regulator frowns on pilots having too many type ratings. There is no specific prohibition against having multiple ratings at once, but the unofficial limit is 5 active ratings.
On the whole, the problem with working at multiple companies boils down to flight-duty concerns, although there is some corporate security thrown in. In your example, if I worked for Ryanair, it is likely I could not go work for EasyJet because they compete. However, I'd likely be able to instruct or work at a drop zone. Yet the main problem still comes down to flight-duty. For every one hour I fly at Company B, that is one hour less I can fly for Company A. And that's just flight time. Once you add in duty time, it becomes a bigger pain. I know a couple of pilots who have had a talk with the Chief because they accepted a flight at Company B and that caused a rest issue for the duty at Company A.