Hooking an analyzer to a processor is a good exercise in learning to use those tools and good for a visual demonstration of some of the properties of the available filters. Also, a knowledge of certain classic filter pairs, such as those that sum to unity or an all-pass is conceptually valuable.

For any real crossover development the electro-acoustic transfer functions of the loudspeakers need to be incorporated into the chain, so this all becomes more cumbersome. My preferred approach, and I assume that of most developers, is to gather electro-acoustic data over a range of angles using a measurement program, process these data statistically employing some judgement and heuristics to create a target electrical response, and then synthesize this response using some combination of mathematical analysis and simulation. Everything except the actual measurement can be done in the comfort of your office without having to listen to pink noise, and even if it's windy or raining.

I write my own simulations in R, many folks these days would use Python, and I'm sure general purpose electrical circuit simulation programs are used, too. Then I go back and measure and listen to see (hear) what I got.

As for classic pairs: There's LR (all of even-order). All odd-order Butterworths (of the same cutoff frequency) sum to an all-pass, the order of which depends on whether the polarity of one of the pass-bands is inverted. And, of course, the 2nd order Butterwoth with one polarity inverted as found in pretty much every old two-way Altec, JBL, etc. speaker. Add to this list.

Best,

--Frank

PS:This works for passive crossovers, too. In this case I measure the electrical impedance to incorporate into the model. I've been playing with using optimization to generate element values for passive filters given a topology and a target response. I'm not really an optimization guy so I've just been using the built-in optimization functions in R, and with a little fooling around, they seem to work.