”Bite” is, like most adjectives in music very subjective. To me, a P bass with round wounds played in anger (preferably with a pick, but finger style works too) is one of the most aggressive bass sounds there is. A Stingray for example have more treble, but less of those scratchy grinding mids. Same with a J bass. A PJ might be an idea but like you said, it’s better to just buy another bass rather than mod your favourite. A lot is eq actually, so a preamp or eq pedal might do wonders. And of course roundwounds is the way to go.