this ’speakerchoices’ link has cool diagrams that give you clues, you can sort by any column, put in limits ...
https://speakerchoices.com/index.html
number of drivers does not tell you the whole story, here’s
a 2 way with 3 drivers
https://amphion.fi/products/helium520/#specifications
a 3 way with 5 drivers
https://www.aperionaudio.com/products/verus-v8t-tower-speaker
the crossover which divides the frequencies, and sends only some frequencies to specific drivers is the determinant regarding 2 way, 3 way,
sometimes a single diaphragm will work with two horns like this
https://products.electrovoice.com/binary/847A%20EDS.pdf
thus a 3 way crossover becomes a 4 way speaker
Tekton V12 is a 4 way with 25 drivers
https://tektondesign.com/product/full-range-speakers/flagship/1812-model-v12/#color
also, you used the word bookshelf, caution, there are very few speakers designed shallow enough to fit a shelf (11-1/2" deep max let’s say), and many have rear vent(s)/port(s) which won’t work in a bookcase.
My Office AR-2ax are 3 way, and true bookcase size, no ports, wire terminals recessed within the 11-1/2 depth, even the rear mounted level controls for the mid and tweeter are recessed. Compact 3 way Bookshelf with 10" woofer. AR-2ax grilles were not designed for easy frequent removal.
KLH Model 5’s, re-introduced, compact stand mounted 3 way, also 10" woofer, are 13" deep, too deep for a bookshelf, they have a single rear mounted level control
JBL L100’s have easily removable grilles and front mounted level controls, a much easier arrangement for adjusting them in place while playing. 12" woofer, too deep for a bookcase