Without any specific experience of the bi-amping craze of the 1990s when some speakers were produced with four terminals to that end I would just throw in some general advice.
The two factors that most affect the performance of a speaker system will be the character of the speaker itself and the character of the room in which they are placed. Speakers generally fall into two distinct types, those which are forward and in the room and the other type which are speakers that seem more neutral and less present. Rooms are either acoustically live or dry. Running extra wires will not produce an improved sound if you are not satisfied with the speakers to start with or have not attended to the issues of placement and room acoustics. It is easier to damp a vibrant room than to add liveliness to a dry room.
It is worth remembering that no speaker, however good or well adjusted, will be equally satisfactory to your ears in every type of music or material. That's another reason why speakers should be carefully auditioned if possible beforehand across different pairs and brands.
On the question of bi-amping it was supported by arguments concerning low frequency distortion arising from integrated amplifiers with a low rate of slew. One solution to this problem is a much simpler and effective route adopted by Philips at an earlier stage - the Motional Feedback Loudspeaker system which still has a thriving fan base in Holland. Each box is essentially an active loudspeaker (carrying on from cinema sound systems in which different speakers were driven by separate power amps) but with the added refinement of distortion detection and cancelling servo circuits built into one or more drivers. Apart from producing a noticeably cleaner and more powerful bass (especially from a smaller box) the overall tone of the speaker was improved.
It may be it is that which you are really looking for so I would suggest you look into MFB speakers! From my experience these systems are not only neat and tidy in terms of design but offer a high quality sound lying somewhere inbetween the two types of characteristic speaker sound mentioned at the start. Stereo separation is also excellent. The only drawback is maintenance - finding a tech who can take them on is very difficult…..unless you live in Holland!
