Before I started with the filter designs I read the book of Douglas Self "The design of active crossovers" that gave me a lot of insight.
Already before reading this book I wanted to do all of the filtering in the digital domain. Why?  because you can... and would be an interresting experience.
One might argue that this will increase the cost of the total system significantly and that the cross-over filtering also could have been done in the analog domain.
All valid arguments but with a DIY project of this magnitude its OK to go for the difficult route in stead of the "easy one".
At the end I had no regrets once it came to the tuning of the filters and the frequency curve of the 3-way speaker system besides the fact that filter responses are absolute and not dependent on passive component tolerances.

As starting point I used an Evaluation board, the "TAS3208EVM_LC" that contains a Digital Signal Processor plus a co-processor in one device optimized for audio processing.
The EVM comes with a piece of PC software called "Pure Path Studio" that allows you to simply drag and drop functions like inputs and outputs(I2S), volume sliders that can be adjusted on the fly when the audio is playing and all sorts of audio processing blocks like  tone controls, graphic equalizers and different type of filters both IIR or FIR.  The EVM connects to a host PC via a USB cable. 
The EVM has four 2mm pitch flatcable connectors. One contains all I2S input signals, the second contains all I2S output signals the third connector holds several control signals which I did not need and the fourth connector holds all analog I/O signals since the TAS3208 also has ADC's and DACs on board.
The I2S I/O connectors are connected to the ADDA board with 10cm long flatcables and the USB connector connects to the IN&LED board to power the EVM from the PAAS module with 5.5V DC. In case of a host connection it also carries the USB data..

If you want to use FIR filters you have to generate your own coefficients and download them in a tekst file. You can use a program like Matlab but that is a piece of software that is not easily accessible for hobbyists.
Douglas Self came to the rescue with Linkwitz-Riley filters built with two 2nd. order Butterworth filters in series that are easily implemented in IIR topology. These 4th. order filters provide a perfect power distribution in the cross-over region.
IIR filters are easy to create with a tool provided in PPS called the "Biquad Filter Design Tool". You can select the type of filter (Butterworth, Bessel, Linkwitz-Riley, Chebychev ), select the order and cross-over frequency.  A graphical representation is also given and the coefficients are calculated.
After you complete your graphical representation of the audio processing blocks you push the compile button and load and the ready to use firmware into the EVM's EEPROM.
This code is non volatile and after disconnecting the EVM from the PC it runs on its own in the EVM, which is what I want for my speaker system.

With my FCA202 Firewire Analog Frontend a microphone plus preamp and the PC software "AudioTester" in MLS mode I measured the frequency curves of my tweeter-, midrange- and bass speakers without any filtering and I adjusted whilst measuring the output levels with the volume sliders in the TAS3208 for equal SPL output.
Later I would position all sliders at 100% output and adjust the output levels with the analog potmeters on the ADDA board to keep the digital resolution of the audio signals as high as possible.
The natural high roll-off of the midrange and the natural low roll-off of the tweeter were as expected a second order but only a few KHz apart.

My initial idea was to put the cross-over frequency for mid and high at 2.5KHz - 3KHz but this turned out an inpractical solution.

When I created the 3KHz filters for the TAS3208, a 4th. order high-pass filter for the tweeter and complementary low-pass filter for the midrange the effect of the natural roll-offs showed up as an almost 9dB dip in the frequency curve.

Here the advantage of digital audio processing became evident. Changing filters is now a matter of seconds without any soldering involved.

My next test was to use the natural 2nd. order roll-off of the tweeter and I reduced the high-pass filter of the tweeter to a 2nd. order Butterworth.
Taking the natural roll-off of the tweeter allowed me toset the low-pass filter of the midrange speaker at a lower frequency and stay away from its cone resonances above 4KHz.
I measured the resulting acoustic output of the tweeter that turned out to be a perfect 4th. order with  -6dB at 2KHz. With a 4th. order low-pass Butterworth filter for the midrange the dip in the resulting frequency curve was completely gone. Further down there is also an off axis frequency graph that shows no dip either, indicating the two cross-over filters do their job.

With a volume of the midrange speaker enclosure just over 2 liters the natural high-pass -3dB point lies at 120Hz with a 2nd. order slope.

When I measured the bass speaker with its servo it was done with a frequency sweep and the microphone directly in the conus what equals to a SPL measurement for low frequencies.
Measuring with MLS pulses works in a non anechoic chamber down to a few hundred Hz, below that you get unpredictable results.
As expected shows the bass speaker frequency curve an almost perfect straight line down to 20Hz. Above 150Hz the mass of the speaker cone  causes the output to drop with a 2nd. order response which is to be expected from a relative heavy aluminium cone.  



The green curve represents the bass speaker output measured directly in the conus, the blue curve is the midrange speaker without high-pass filtering (also measured directly in the conus).

The tuning of the bass speaker that is mounted at the side of the speaker cabinet, its low-pass filtering and the midrange speaker high-pass filtering took several iterations before I was satisfied with the results. Because MLS measurements are unpredictable below 200Hz and the loudspeakers had to sound at their best in my livingroom I decided to conduct listning tests there using my ears as measurement equipment.
After several changes in settings I concluded that a combination of a second order high-pass for the midrange at 100Hz combined with a 2nd. order low-pass at 150Hz for the bass speaker gave the best results.
Other settings resulted in a somewhat thinner sound experience in the lower region for instruments like piano's and male voices.

The first filter in the system is a 4th. order Chebychev high-pass filter at 35Hz to filter out any DC and subsonic frequencies.

Finally I put all the digital volume settings back to 100% and ran a repeated MLS sweep to adjust the output levels for mid and high with the potmeters on the ADDA board to maximize the digital resolution of the audio signal.

The system sounds natural and small tweaks to get 1-2dB bumps ironed out in the frequency graph didn't make it sound better so I just left it like that.

Below the Pure Path Studio generated filter structure block diagram and the MLS plot over the full frequency range at 0 and 30 degree axis.