Here we see the schematic for a basic two-way, 12dB per octave passive crossover that is set up for biwiring.  This crossover is identical to the other, except that the filter's inputs have been separated.  The tweeter and woofer sections of this loudspeaker are now two separate speaker systems.  (Although this configuration is very rare in PA gear (SLS offer it as an option) it is very common in Hi-Fi loudspeakers.)  This gives us two upgrade options prior to making the leap to an active configuration.

Step 1) We can biwire the loudspeaker.  Instead of using one two-conductor speaker cable as is normally done, we use two two-conductor cables (or one four-conductor cable).  One cable runs from the amp to the Highs Input, the other runs from the amp to the Lows Input.  Owing to the higher resolution of a Hi-Fi as compared to a PA, the advantages are greater in a Hi-Fi, but it does sound a little better in a PA.  And, the cost of 12-4 speaker cable is not that much more than 12-2 cable.  It's a cheap upgrade.  Plus, when you upgrade the system to active, you can use these same speaker cables.

Step 2) Once we have biwiring taken care of, we can then passively biamp the speaker.  Instead of using one channel of amplification to drive both the Highs and Lows of the loudspeaker as is normally done, we use two channels of amplification, one channel (and speaker cable, of course) for each section of the loudspeaker.  Both amp channels are fed the same full range signal from the mixer (or EQ, etc.).  The frequency division for the drivers is handled by the passive filters.  It would seem that there would be nothing to gain by this, but there is:

The input impedance of the highs section increases as the frequency decreases, so the highs section draws less power from the amp as the frequency decreases.  The amp that is driving the highs is now doing a lot less work than when that amp was also driving the lows section of the loudspeaker, where most of the power is used.  (The input impedance of the lows section increases as the frequency increases, so the lows section draws less power from the amp as the frequency increases.  But as the highs use much less power than the lows, the performance difference in the lows section is pretty small.)

Overall, the advantages of passive biamping are much the same as the advantages of going active, the improvement is just smaller.*  This is mainly owing to the power loss and distortion in the passive filters.  Once you have passive biamping taken care of, when you upgrade the system to active, all you have to do is remove the passive crossover from the loudspeaker, put the active crossover in the amp rack, and tune the system.

* Not all passive crossovers contain simple filters.  Some have significant frequency response and other "tweaking", therefore going active can in some cases actually degrade the performance of the loudspeaker.  In such a case, a digital crossover (DSP) is required, as the DSP can be tuned to emulate the "tweaking" that was done in the passive filters.  (The DSP can actually do much more, but as there's plenty of information about that available from the speaker and DSP manufacturers, I'll let you learn about that from those folks.)