You can (1) Bi wire or (2) Biamp.
(1) Bi wiring means you have two pair of wires going to ONE speaker connection on the amp. They are a parallel connection. At the speaker end one pair goes to the HF connection ( tweeter) and the other to the LF (bass speaker) connection. The wires could be the same type for both or you can use a smaller gauge ( diameter of individual strands ) for the HF , tweeter section, and a heavier guage for the LF section. How different this would sound is not always predictable but you have to try it out. But the last suggestion could be preferable. There is a recent post somewhere about choosing wire guage somewhere on this forum. AND , ALWAYS keep your wires as short as possible ! Don't keep extra lengths coiled up . If you have extra wire then do all the testing and then finally cut it to the exact length you require.
Does this sound better than just one pair of speaker cables ? When I tried it I found it did . But there are others who say they hear no difference. If this interests you , you MUST try it in your system and see what YOU think about it.
We had a pair of Dynaudio Audience 50 speakers that sound very good. Apparently Dynaudio said that it had only two terminals because biwiring didn't make a difference. But then who in Dynaudio said that or was it just a marketing blurb to explain away the lack of biwiring at this price ? So since our experiments with other speakers showed a difference we decided to forego the warranty and pulled out the terminals and installed a biwiring socket in its place. We had to chop up the pcb tracks on the crossover to separate the ground of the woofer and tweeter and had to enlarge the hole on the cabinet to accept the new biwireable socket. This would also kill it's resale value !
So one speaker was now biwired and one was in stock condition. We tested/compared them individually for quite a long time. The biwired one DID sound better. Not chalk and cheese but the biwired one was a step up. Mainly in the HF region.
Just a note on speaker cables. The ones that are good ( like a bunch of enamelled wire of proper guage ) can bring up the HF performance in a subtle way and percussion/drums can get a snap to it that wasn't so audible earlier .
(2) Then you have biamping . This is more expensive. You need another stereo power amp for this. One power amp is connected to the LF speaker terminals and the other amp is connected to the HF speaker terminals . With separate speaker wires of course ! However there is a small catch here .
The two amps must have the same 'gain' or adjusted to have identical gain while being connected to the same source . There are other small pitfalls too.
Now both power amps inputs are in parallel , so the effective input impedance is smaller , typically half of what it was earlier if they had similar input impedance. This will change the low frequency roll off. That may or may not be audible. Maybe not, in a good amp. You also need a Y connector to the external preamp ( or preamp output on one amp ) and connect one lead to one power amp input and the other to the second power amp . As you can see its getting more complicated now . Setting the gain to be equal on both stereo power amps is essential. If not , you will need to attach a variable potentiometer ( a preset or volume control ) to the more sensitive amp's input ( if it has no volume control of its own at its input ) and reduce the input level. Needless to say you need to know what you are doing AND a meter to check this.
So does this sound better than scheme (1) . Yes it does . Its much better and the difference is very audible.
(3) the third possibility is to use an active filter that " matches the curve of the stock crossover when loaded with the corresponding speaker driver " and then remove the internal passive speaker crossover altogether . Yes ,sounds even better ! But then it's not for the faint hearted AND you need test equipment to do this properly ! At least a signal source and an ac mV meter. Typical DMM's will not do this unless they specify a bandwidth of at least 20 to 20 Khz and those are expensive. MOST are good only up to a couple of kHz and LF performance is not accurate very much lower than 50 Hz. But there are software solutions also on the NET.
Active systems sound much louder than the existing passive system AND sound cleaner over the whole bandwidth . A 20 watt per channel pair of amps will sound amazingly loud and clean ! There is a reason for this and its all about maths !
All this requires plenty of free time and a knowledgeable companion, if you don't know what to do yourself !
However it IS an enjoyable experience because the end result can never be poorer than the start and most often is audibly better !
However its good to start with the speaker cables and biwiring scheme ( item 1 ) as it is the easiest to do and you get to know if it does make a difference in your system.