Boy, that's an old one.
Jerry Gebby, Father of the .22 Varminter (.22-250) did a piece on converting the M39 to .38 Super about 40-50 years ago.
Yes, it is possible to ream out the M39 chamber to accept a .38 Super cartridge. But then you have pretty much a wildcat. The magazine won't take standard .38 Supers so you have to handload short OAL ammo for it. Gebby recommended 90 grain bullets to fit the clip and give high velocity.
He also pointed out that after the brass was fireformed to the tapered chamber, it would hold more powder. That would make most people nervous in this day and age of concerns over "supported chambers."
I wouldn't do it. High end 9mm is pretty close to .38 Super anyhow. You have to go to the big loads to show an advantage for the longer case. Remember that sloppy chamber?