Hcfyk

It's a matter of preference, but I would float scrap lumber backing at four locations:

1. Down both sides


2. Across the bottom between the two studs


3. Across the between the two studs just below the plumbing penetrations


4. Anywhere else that seems too flexy when you do a little press-testing

1/2" or thicker plywood and 1-by or 2-by lumber work well. This backing doesn't really need to be attached to the studs in all cases (doing so can make it difficult to keep everything flush), but should be fastened well to the surrounding drywall. Construction adhesive would reduce the number of screws necessary there.

Protip: If you don't have access to a dedicated screw gun (which is not the same as a drill, despite common usage of the term), these drywall screw setter bits are golden because they keep the screw from sinking too far into the drywall:

I don't ever attach drywall unless it has attached backing on each side. To float the backing and have it come out solid and flush and not cause drilling issues is both a thing that needs to be practiced and it needs the appropriate access.

For something like this I would go to next stud for sure. Also I would build a little access box jutted out from the wall maybe 8" or so. Here is the deal if you float this and bump into the area it could crack - I hate working on something prone to failure especially in an area that has usage. A proper access box of maybe 20" tall by 8" out would allow you to service these turnoffs properly if there were issues without opening the whole wall up again. Also if you have to turn these off you are probably putting pressure and a good chance of damaging wall area behind it. I honestly have only seen this a handful of times in houses.

My answer:

1. Remove drywall until you can go to studs - almost no extra work and much faster and long-term than floating. If you can't do this then add an extra stud - it does not need to go higher than hole. You can add two support blocks.


2. Build an access box (2x2s) and attach across framing.


3. Drywall access box and hole.


4. Be glad you did it right.

One option is to glue and screw plywood to the back of one piece of the plaster board, creating a ledge for the other piece to be glued and screwed to. Predrill into the ply to reduce the forced needed to get the screws started and use very sharp screws.

Do likewise around the hole where possible.

This will result in all edges being surported.

If you got enough depth wood can be used instead of ply.

It appears to be supported by two studs. Unless you want to make a bigger patch (& hole) that goes halfway on to the next studs on either side, just screw it into the two studs and start mudding and taping.

Edit to add:
Leave about 1/8" (3 mm) gap, knife mud into it, embed tape into mud on the surface (paper tape actually makes a stronger joint, unless you are using "setting" mud rather than the usual drywall compound that dries) and mud over that until you are happy with the appearance, using progressively wider knives and knocking off any high points when dry, before applying the next coat.

If you're joining drywall, I've found a good rule of thumb is if it's not within 3" or so of a stud, you need something to attach to the drywall behind the drywall. That's what Isherwood is referencing in his answer. The idea is that, if something hits a section of drywall, you want something to reinforce it, or you'll be back patching a jagged hole.

Scrap lumber is great... if you have scrap lumber laying around. If you're not doing stuff like this on a frequent basis, you might not have any. If you don't, a good and cheap solution is to buy a pack of wood shims (typically found in the door and window section of your hardware store). Be sure to cut the narrow end off the shims if you go that route. You will need drywall screws for this as well.

The catch with screws is to not "over-drill" them. You want them to sink just below the surface of the drywall, but not drive straight through the drywall itself. Worse for you is you'll be doing this on a live setup. Hopefully you have a driver that drives slower the less you squeeze. Just take it slow and you'll do fine.

As for location, I would do 2 in the top right (where the cuts jog further out), and one vertically to the left of the pipes along your cutout.

Additional tip: draw lines on the wall where your studs and supports are. It will help you a great deal in hitting the supports.