Adding a tweeter to a full-range

I'm using 4" full-range whizzer cone speakers in my bedroom. They operate normally. No lack of treble. However, one day, I found the NOS tweeters of the same series with those full-range are being sold. I think what if I buy and add them to the 4" full-ranges.

Of course, the HPF for the tweeter is required. But, how about LPF for the full-range, isn't it required?

If so, the x-over point might be set at around 4-5kHz (no problem). But, if not, which means running the full-range (closed) to 20kHz as usual and assigning somewhere upper frequency for the tweeters to handle, then, what frequency should be set for HPF of tweeters?

PS. I have a DSP in my system so I can actively control x-over.

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A measurement mic analyzing the drivers responses would answer pretty much all your questions.

4-5khz is probably too high of a xover point. Generally you want it to be as low as the tweeter will allow. The distance of the drivers from one another plays into the xover point as well as the drivers dispersion. Too high of a xover point can leave one with a very beamy woofer.
 
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