The foundation may not pay rent to the family office, because the family office is considered a disqualified person, and that’s not a personal service. However, a foundation and a family office can share office space, provided that the person to whom the foundation is paying rent, i.e., the landlord, is not a disqualified person.
So, if it’s a third-party landlord, and you go into a shared lease where you’re each paying a relative portion, this may be allowed. However, you have to be careful about breaking an existing lease, but if you’re talking about new space, it may very well be possible to go in together with the landlord. You can say, “We’re going to rent 10% and they’re going to rent 90%,” and you each have a lease agreement. But you cannot lease from a disqualified person.