The first thing you need to do is to read about Linkwitz-Riley filters. It concerns filters that are phase coherent at the transition frequency. The original application was loudspeaker crossover filters, but can probably be used in your case as well.
I attach a sketch of how the principle of an active LP/BP/HP looks.
It's a combination of low pass and all pass filters with summing amplifiers. The circuit has phase coherent outputs over frequency that can be summed without problems.
LP 4. = 4th order low pass
AP 2. = 2nd order all pass
Important to note is, that the 4th order LP sections do not have "normal" 4th order responses, but 2nd order squared, meaning two identical 2nd order sections with the same cut off frequency and response cascaded. Otherwise the LP and AP phase responses will not track.
The LP filters can be Bessel, Butterworth, whatever.
Have fun

EDIT: you can achieve the same functionality with "normal" LP/HP filter topologies, but it's somewhat challenging to calculate/synthesize.