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Double Bass extra speaker within

It would likely cause a lot of feedback earlier in the SPL scale, as it would make a big bulge in the frequency response that would interact unfavorably with the primary body resonances of the double-bass.

To avoid that, you need sufficient internal space and to maintain proper tuning in the enclosure for two woofers - and not just halving the existing space between two drivers.
 
Timo,

The answer is that, no, it would likely not work very well at all, although there's no reason from the standpoint of the physical acoustics to expect the effects that greenboy thinks are likely without knowing very specific details. Feedback "earlier in the SPL scale," I suppose means greater susceptibility to feedback in that he thinks it would be induced at lower levels of intensity. This depends very much on the particular resonances excited between the DB and the cabinet as it interacts with the surrounding surfaces. Again, not enough information. It would be quite likely, almost inevitable, that the frequency response of the system would become erratic. Whether that would be manifest as a "bulge," that is, a broad peak, a narrow peak, a trough, ripples in the spectrum depends, again, on the specifics.

There are many ways for this to go wrong and few for it to go right. There are many, many parameters to be considered and a configuration of the type you describe is best designed from the ground up using a computer to help in the alignment and tweaking.