I actually haven't seen the term multitimbral voicing to describe multitrack recording on a keyboard. Lots of keyboards include the ability to have 16 timbres on 16 MIDI channels (which I think would qualify as mutitimbral voicing)... in fact any GM compatible board can do this, but that does not mean they include sequencers with the ability to overdub one part over another. But yes, any board called a "workstation" can do it, as can many boards called "arrangers" since they often also incoporate "workstation" functions.
But to the issue at hand of wanting to include AUDIO tracks along with your sequenced instruments, that has gotten more rare, I guess as people have moved to computers for that. Korg Kronos does 16 MIDI tracks + 16 audio tracks, but is out of the price range, and has no on-board speakers. An inexpensive older keyboard that might do what you want is the Roland Juno G, which supported 4 stereo audio tracks in it sequences, along with its 16 MIDI tracks. (Still no speakers included, though.)