You could do it sort of like the Dvati, where some of your actions take up the actions of all three bodies, whereas others can be used once for each body. Then also make it so that limited uses of abilities and resources are also shared (such as per day or per encounter abilities, maybe even hit points). I'd go with move and free actions being usable by all bodies independently, but giving only one full-round, standard, swift, and immediate action across all bodies (when you choose to take them instead of move actions). You can refine when actions are shared or split based on the specific actions performed, but that's a good baseline to start with. Given the extreme importance of the action economy, be very careful with this aspect to not let any loopholes get through, even other homebrewed material. Even move actions shouldn't be freely shared, as there are several existing homebrew and even printed abilities that can leverage good use out of those actions.
Another thing to consider is letting the three bodies all be affected by the same spells like the Wizard Familiar/Druid Animal Companion ability to share spells.
