Hello, to help a bit with your question usually some roaches may get along better together than others. A concern with cohabitation of species is one species outcompeting the other for food/hiding places, etc. Some would thrive and the others would dwindle down in population, but since you don't intend to have them reproduce it may be possible to house multiple species together and have them coexist to an extent. There may be aggression between different species, but I have no evidence myself. They may stress each other out, but they don't seem to get lonely if not able to breed. I had a single female Deaths head roach live for over 3+ years in her own enclosure. Just recently lost her.
Another concern is different microclimates/care. Some species may require much different husbandry needs than what another species may need (humidity, temperature, ventilation, substrate depth etc.) so there can be conflict on that end as well. Some aren't super picky. I've heard of others that have successfully kept different roaches together, but not sure how it may work out in the long run.
I myself haven't really mixed species, but maybe some others with more insight/experience can pitch in better information. I've heard of Blattidae sp. "Kenya" aka "little Kenyan roaches" getting along with other larger species of roaches due to their small size and tolerance to different conditions, but i have no proof of this unfortunately. So it could be false