You can do it yes. I did 3 plants in same 2x2 before, 2 of 1 strain, and 1 of another. To make it work you will need to flower the plants when they are pretty small (im guessing 6-8"). Expect them to double in radius when you flip to flower and get 2-3x as tall depending on strain. You will probably need to do some LST to make them stay out of each others way and fill your space better.
I wouldn't recommend it though. It becomes really challenging because each strain will need different light intensity, nutrients, and training. If you do run more than one plant, ideally they are all clones from the same mom, so that they grow similarly. Even different phenos of the same strain can grow very differently.
I think if you focused on doing 1 large or 2 medium sized plants in the 2x2 to start it would make things a lot easier and increase your chance of success (and probably yield as well). Then just grow the next strain on the next round. Cannabis requires a lot of patience at all stages so I would relax and know that you have more beans in the stash, and make things simpler on yourself at first.