I ran into this problem when I ripped out my interior doors and purchased pre-hung doors from the big box stores. All of the pre-hung doors they sell come with 4 1/2" jambs which work fine for newer homes build after the 70s that come with 1/2" drywall.
My home built in the early 60's has drywall/plaster hybrid walls and these measure roughly 7/8" thick which means I needed jambs roughly 5 1/2".
The easiest approach if budget is not a question is to order pre-hung doors with the correct jamb size. These doors will be roughly $60-100 more than the ones you find in stock. This is sometimes a difficult pill to swallow knowing that it's going to cost you $1000 more for jambs that are an inch wider.
I was determined to find a more cost effective approach at the expense of my time and labor as that is something a DIYer has a lot of.
First, I disassembled the jambs and cut about 1/8" off the non-hing side to remove the factory radius and the primer leaving raw wood.
I then purchased a couple 4 1/2" non primed jamb kits and cut them to width. next, I used a 1/8" roundover bit in my router to cut a radius on my cut strips to match the existing jamb radius.
I then glued and finish nailed the extensions onto the jamb. I used two pieces of plywood to clamp them before nailing so they're flush with the existing jamb.
After the glue dried, I sanded them down with a block sander to make them absolutely flush, applied a light layer of joint compound and finished with a light sanding. primed, painted, reassembled the jamb and hung.
Was it a lot of work? kind of but if you have all your jambs apart and do all the steps in order, it's not so bad. Of course you need a table saw, router with correct bit, nailgun and clamps.
What you don't want to do is slap on a piece of wood over the primed jamb and fill the gap with joint compound or else 100% chance it will crack (I know because I tried). Another option is to use a filler piece after the door has been hung and "step" it back about 3/16" and then caulk the seam. I didn't want to use this approach as I don't particularly like the look. Good luck.