Yes it's possible!
I have bought and sold more than I care to think about since starting BC. However when it comes down to it I really like the idea of having a bass that's 'me' - my sound, and what I use for everything. Kind of like some of may favourite players have had a bass which they are known for playing. It's a nice place to be, because otherwise I was always second guessing which bass I should be using for what and it became a distraction. So after years of this cycle (which, although I wouldn't want to go back to that now, was a great way to try out lots of instruments and learn about what I liked) I realised that one bass always ended up back at the top of the pile and the others got sold or swapped.
To this day I still have that 'one' bass that I know is just perfect for me, but it doesn't 100% stop me wanting to buy and experiment with others too, so that way I look at it is that I have MY bass, and sometimes one or two others that I play with for fun, but I never buy them for keeps, and can easily slim right back to that one bass at any point.