The most simple way to activate an existing speaker is to measure each driver nearfield, first with the crossover connected, then, with identical settings/ mike position, but no crossover connected. This eleminates any room issues.
Next you start to program the DSP, same setting and mike position, to match the recorded curve.
From the recorded measurements you (or someone who knows) can see what filters Revel created in the passive x-over.
If you match them, the sound should improve a little, more clarity and attack usually. How much depends on the amp and the passive crossover. You eliminate any sound issues of passive components and ease the load on the amplifier(s). Even the most stuborn "passive is best" fractionist can not deny this.
If you do identical filter curves in the nearfield, the in room response should not change with this method. You keep all the advantages and faults the speaker had in passive mode.
Next step can be to optimise the filters if needed. If you want to to do this right, you need advanced measurements, not only near field. This is serious stuff and you need free field, different angles and distortion tested. Then enough knowledge to do better filters, crossover frequency etc.
In general, any passive crossover is a compromise of limitations the parts budget and the manufacturers policy allows.
Number and quality of x-over parts is a typical playing field for the guys with the red marker to save costs.
Part quality is very much overrated, once you remove the known junk, boutique parts don't improve anything noticeable.
Parts number and size is another chapter, the smallest PCB with the least components that still sounds acceptable wins in a commercial products. This is the area where a good developer can make huge improvements over the passive version. Be warned, this comes close to a complete new development!