It is possible (for an unusually knowledgeable travel agent), but not easy.
There are two fields in the PNR for each airline, the FQTV field (frequent traveller number for mileage earning) and the FQTS field (frequent traveller number for status purposes).
These can be set to different values. But airline IT systems are not always designed to understand that this can happen, so even if you manage to find a travel agent who understands what you are talking about, it is not guaranteed to work.
If you use a tool like the free MyFlights tool, it will tell you which numbers you have attached to the booking and whether they are FQTV or FQTS (or another type of FQT number). MyFlights is only available for Amadeus bookings.