The JBL specs for the 2235H say that you you shouldn't use it above 1khz (paraphrasing here)
The JBL specs for the 2446 say that you you shouldn't use it below 500hz.

Why can't they have a "common area" of sound reproduction? Would they interfere with each other somehow?

Why not have a low pass filter which would start rolling off the 2235 just before 1k and a high pass that would roll it off at just above 500hz. So they would have a common area of 500-1000hz

Is that a big no-no?