Yes, that is what I do. I get bored easily, so I like to change things up, and changing your routine helps you work through training plateaus. But I also have some exercises that I love, and some exercises that I can't do (they hurt when I do them.) So rather than completely change exercises on a regular basis, I like to mix up my loads and rep patterns, or change my exercise order, or combine my muscle groups differently (chest-lats/legs/arms-shoulders combination for a while, then switch to pushing/pulling/legs for example). Or switching all of the above. (There are a lot of different variables and combinations you can switch). This way I can still do the movements I like, and avoid the movements that hurt, and I am changing my routine often enough to not get bogged down.
I also limit the number of days I train, so that I can have a life outside the gym. Changing my training frequency is no longer one of my variables, at this point in my life.
One of the biggest breakthroughs in my progress was learning about varying my rep ranges (and weights). I try to cycle through various rep ranges and weights every workout. Meaning that one day I do heavy weights and low reps. The next time I do the same exercises but less weight and higher reps. I find that my 'heavy' 'medium' and 'light' days are synergistic. My heavy days make my medium days seem lighter, and so on.
I am certain that I read about how this works on T-Mag. Try doing a search on the words "adaptation" or "rep cycles" and see if you can get a more scientific explanation.
I don't necessarily recommend that you limit your exercise selection... I do it out of necessity. It is a good thing to be able to do a wide variety of movements. But I've been training for a while and I have little injuries to nurse and some movements are off limits for me.