Yes it possible on most airlines if you go through an agent.

Alternatively… you can go Future.Travel Best travel website for airline tickets No Booking Fee and select multi-city ticket.

Select the leg(s) you want to be in business class, and select the legs you want to be in economy. Pretty simple.

The cost may surprise you as in some cases the business class ticket option will come in below a standard economy ticket. Not a miss print… just how the fare combinations may work given heavy economy class loads or promotional sales on by an airline that may not be published to the public.