I guess it could be possible? (unless its an eternity perhaps)-- I had a ring, kinda like yours-- I wanted to add a bezel (replacing 4-prong)
they basically cut the ring down the middle-under the prongs, opened it up for a basket (took extra metal from the back of the shank.. it wasn''t an eternity) and welded the bezel basket in
I think yours will be more difficult -obv. because it involves diamonds, but also because you''ll probably want the halo to mimic the pave on the shank of the ring.. (could be difficult to recreate- without looking weird)
It really might be easier to get a new setting
If you do decide to alter (if its possible)-- I would email several vendors -- for me- some said it would cost about as much just to construct an entire ring from scratch.. others quoted 1/4 of this price