Passive crossover design is much more complicated than you would think.
Yes the parts (capacitors, coils, resistors) are readily available. And software to do calculations is, I assume available. 15-20 years ago when I first got into speaker building I bought a $10 DOS program to do calculations. And there was a program called LEAP for about $400 that was the top of the heap ( I never owned LEAP and not sure if it is still on the market) and several others in between. Today there are probably lots of options for crossover design calculations including software and you can even probably find formulae to do calculations manually (not recommended). But that is where the easy stuff ends.
You also have to do the following:
1) Determine the best crossover point. Set it too low and your tweeter will be vulnerable to damage. Set it too high and you lose dispersion for a band of frequencies because the woofer tends to beam frequencies at the higher end of its range. How will you choose the crossover frequency?
2) Determine accurate impedance values for your drivers. Just because the speaker is stamped "8 ohm" or "4 ohm" it doesn't mean you can use these values for design work. These are nominal values and likely not even close to the actual impedances that would be used for calculations. For example, a nominal 8 ohm driver can have actual impedance of around 6 ohms. But you don't know until you test it. It is essential to have the actual impedance to make a crossover that works correctly...otherwise your speakers will sound horrible (believe me, I have learned this the hard way, lol). To complicate matters further, for a 3-way system (which I understand yours is not) the mid-range driver will very likely have a significantly different impedance at its lower and upper crossover points.
3) What about level matching? Your tweeter may be louder than your woofer, or vice versa. Speakers manufacturers typically incorporate resistors in the crossover to properly match the outputs of the drivers in use. How will you match the level of your two drivers? Trial and error? Every adjustment you make will require a change in the other components of your new crossover.
4) Choose a crossover slope. There are trade-offs here. As the order of the crossover increases you get better protection for your tweeter and a smaller band of frequencies being produced by both drivers. But you pay for that in loss of efficiency. A 4th order crossover (generally) has 2 capacitors and 2 coils - with 2 elements in series with the driver and 2 elements in parallel. These things suck energy that would otherwise be used to produce music in the speaker.
I am only vaugely familiar with AR speakers. Are they not known for being efficient speakers? (please someone correct me if I am wrong about that) Anyway, efficiency is a very good quality for a speaker to have. It makes it possible to get good sound from lower powered amps and receivers. Now if you have a 200 watt amp maybe this is not an issue. But at 50 watts or less I would say that any speakers with a 4th order crossover may not be a wise choice.
I am not trying to discourage you or anyone from learning about or designing passive crossovers. But to do it right requires lots of testing, lots of equipment, lots of knowledge, lots of time. It is very easy to mess up a good pair of speakers. A proper crossover is critical to good sound. And the AR guys have already done this task for you.
There are lots of posts (either in DIY or the Speakers sections of AK) that discuss replacing capacitors in speaker crossovers. That operation is relatively safe and may even yield improvement in sound. May be a good place to start.
