I think you can if you give them the endorsement. Now not every multi is high performance, so just because you can solo a student in a multi does not blanket cover this question.
I was a member at an AFB Aeroclub and they soloed students in the T-41C all the time. It is basically an Air Force Trainer version of a 172 with 210hp, and it was an s-load of fun to fly. The only thing was that the Instructor needed to remember to give the student their HP Endorsement as well as the other required Endorsements.
I've trained several people for their private in C182s and the insurance company had no problem with it. It's interesting because, in the long run I think these students turned out to be better pilots. People who train in lower performance airplanes and then buy a high performance airplane tend to be way behind the the aircraft since most of them barely get "checked out" in their new birds.
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