Normally, there are two reasons to bi-amp. One is to effectively increase the power that one has. This can also be done by just getting a more powerful amplifier without bi-amping. If your system plays as loud as you want without distortion, then you don't need more power.
The second reason is to bypass the passive crossover in the speaker (or when there is no passive crossover and bi-amping is necessary). This is done with an electronic crossover, where one feeds the preamp signal to an electronic crossover, the high frequency output of which is fed to one amplifier and the low frequency output is fed to another amplifier. The crossover frequency that is selected needs to match the capabilities of the different speakers (i.e., it must not be too low for the tweeter [or midrange] speaker, and not too high for the woofer, and the crossover slope must be appropriate for what is being done as well). This can result in better sound (particularly if the passive crossover is poorly designed), but one needs to worry about whether or not an amplifier inverts the phase, and one needs to carefully match the levels of each for proper sound, so if one does not know what one is doing, there is a decent chance that the sound will actually be degraded by doing this.
Now, as for whether what you are proposing would work, you should consult the manual for your speakers about how they are wired and whether or not they are set up for bi-amping or only bi-wiring. (If they are set up only for bi-wiring, forget about it, unless you are planning on rewiring the internal crossover of your speakers, which, unless you really know what you are doing, you ought not even consider doing.) You also would want to bypass the crossover in your speakers if you are using an electronic crossover, or you will be applying two crossovers which will interact, most likely in a manner that degrades the sound. If you don't have the manuals or a reliable source of information regarding the crossover frequency and slope that would be appropriate, I recommend that you forget about it and just enjoy it wired normally.