So, I always love the look on P bass, been dreaming to own one. Before, I have Sire V7. Last year, I bought a Fender P. But, after making band and in a band situation, I rely on the V7 more, which is a Jazz type. She makes me create interesting bass lines more for my original material. I always consider myself as a P person. The question is, am I, deep down, without realizing it, more J person? Should I bought a Fender Jazz next? Lol
I think I'm similar to you - I like Jazz basses, but I got a P/J bass a few years ago and that instrument has been very helpful with my sound in my current band setting. The tone of this specific instrument can sit very well in the mix, especially when I play it with the P pickup solo'ed. It also fits me rather well. That means that I can play it comfortably - almost as comfortably as my favorite Jazz bass.
But I've owned several different basses through the years. Although I think that I'm naturally a little more of a J than a P player, I've tried and also bought both good and not-so-good versions of each type. Even if you think you're more of a J player, I'll bet that there are some Jazz basses out there that won't work for you. There are probably at least one or two Fenders among them.
I think that the great news is that you have that Sire V7. That's a rather good Jazz bass - I bought one last year after I tried it and I liked it a lot. The only reason I returned it was because I already had two other Jazz basses. After a week of comparing them all at home, I realized that the Sire wouldn't replace either one.
Since you already have a good Jazz bass, I don't see any reason for you to get another one. You might find that several Fender J's don't work for you as well as the Sire that you have now. If you try a specific bass and you love that specific bass, then I'd say get it. Just don't assume that you need a Fender.
Also consider that if you pick up a second J-bass, one of them might go unused. I love my different basses because they're different, but I also play all of them because each one of them fits me well and gives me some different sounds.
I should add that although I have two J-basses, one of them is loaned out to my pal's daughter who is taking up the bass, too. I was worried that it was too heavy for me, so I picked up a much lighter alternative to experiment with for a while. I'm glad that I tried this, but I'm missing my old hefty J and I'll probably get it back in the summer (or build another one just like it).
Keep trying different instruments and pay attention to their shapes, dimensions, and how they individually fit you. Your preference for J-basses could be rooted in your comfort with a more narrow neck. I'm not too comfortable with a traditional P-bass neck with its extra width, but I've also found some J-bass necks to be so narrow and shallow that they didn't fit my fretting hand very well. My favorite Jazz is 1 1/2" wide at the nut, but there is some extra wood under the finger board and it feels chunky enough to fit me very well.
It's great that you have a P and a J of some sort. If you like one more than the other, that's also great. If you feel like you have to make some sort of choice though, I don't think that's the case.