We did this for several years with a small private school. They were perfectly happy to have a student for 1-3 days a week (depending on the year; we tried various arrangements), for slightly more than prorated tuition (e.g., half tuition for 2 days). Our agreement was that their teachers did not have to provide any grades (we treated this as homeschooling, as far as compulsory schooling goes), and our child would have the option of participating in any classroom activities that the host class was engaged in on school attendance days, but that they were not obligated to do so.
After we had been there for a bit, they formalized the arrangement, so that other students now can enroll for any number of days, with the option of parent- or teacher-graded classes in any number of subjects. I admit that I may have had something to do with the development of the formalized program.
If you want to know specifics of the program, pm me.
