The bad news is that when you cascade two crossover filter pairs to create 3-way crossovers (passive or active) they tend to run into summing problems right from the start. Even ideal electronic summation often results in response aberrations that strongly depend on the spacing of the two crossover frequencies and the filter type. As a rule, the more widely spaced the crossover frequencies the more accurate the summation. As you move your crossover from the ideal world of electronic summation to the much more difficult arena of acoustic summation the problem grows. You now have to consider not just the responses of the crossover filters but the responses of each driver in combination with the crossover filters.
There is one wonderful exception to the generally nasty behavior of 3-way and higher crossovers: the 1st order Butterworth crossover. The ideal performance of this simplest of all crossover types holds up even in 3-way and higher crossover types. The electronic summation characteristics are absolutely perfect. This crossover sums to deliver not only a flat frequency response but a flat phase response as well . . . regardless of the complexity of the crossover. This essentially perfect behavior of the first order filter pair once led me to use them for a 13-way crossover I designed for a consulting client in the recording industry. Yes, I said 13-way!
So what can we do? Well, here are my suggestions for getting good performance from multi-way speaker systems.
First, I recommend avoiding anything more complex than a 2-way system whenever possible. Always be reluctant to add another crossover.
Second, if you must add another driver and crossover in order to reach your design goal then try to keep the crossover frequencies spaced as far apart as possible. My circuit simulations show that the combination of a 1st order Butterworth with a 2nd order Linkwitz-Riley (as in the above example) results in a 3 dB dip below the crossover frequency when the two crossover frequencies are spaced two octaves apart. Spacing the crossovers three octaves apart (250 Hz and 2kHz for example) reduces the theoretical best case error to -1.5 dB. Increasing the spacing further to four octaves reduces the error to just -.25 dB. Combining two 2nd order Linkwitz-Riley crossovers results in summing error as great as 1 dB even when the crossover frequencies are spaced at four octaves.
Third, use 1st order Butterworth crossover types for as many of the crossovers in your multi-way system as possible.
