How do you bring your companions with you on hunts?
Just in case you didn't figure this out or if anyone further is curious about this: Make sure you've gone to "team" in the research section and upgraded "More girl teammate" in that section, each rank gives you +1 slot. Now with that done go to the crossed swords (Companion) section of the tech menu. Once you have a corrupted girl you will then have her shown here, and by default her portrait will be dark. You simply left click on the dark portrait to add her to the attack party roster.
Be really careful not to click again, because in some versions setting a girl to non active from active will still consume the roster slot...forever. The same is true of tentacles you add to your party, just you buy the 'tentacle' tech point levels rather than the girl teammate option.
Now if someone's stuck on actually corrupting a partymember, you need to go to the build menu from right clicking the floor and selecting option 2. You then select a captive and it will start a corruption animation with a bar that goes up. Once the bar is full you right click her and then press the thing that looks like a 'play' button in the middle, this will clear her off the floor and place her in the roster window.