No construction adhesive. I'm assuming that you are using cabinet hanging screws? One properly placed cabinet hanging screw that is fully engaged into the hanging rail and stud is sufficient, as long as the cabinet is properly attached to it's neighbors that are also properly attached to the wall with any voids filled with proper shimming. If you feel that you'd like additional holding power, blocking at the ceiling that will be hidden by the crown can be used.

Be 100% sure that you can get all of this level in all dimensions, with the proper shimming, and that the front of the faceframes lines up all the way across the run without any of the cabinets being racked. Proper shimming isn't just >. It's also

Sorry, but your description and questions here says to hire an actual cabinet installer. Immediately. You can very easily be in the group that makes 20K worth of cabinets look like 2K worth of scrap lumber rather than 2K worth of stock cabinets look like 20K with a craftsman like install. You're being penny wise and extremely pound foolish.

Cabinet installation is SO much more than "just" screwing boxes to the walls!

When demoing our old cabinets, I discovered that the cabinet that held all of our heavy stoneware dishes and bowls wasn't attached to studs. At all. It was just screwed into the plaster, and not with anchors, either. I have no idea how that cabinet didn't come crashing down, but it held up for over 25 years. I think what you are proposing -- attaching to one stud and the adjacent cabinets will be fine.

The difference in many older cabinets and new ones is that many older ones had load bearing backs, and you could get a screw in anywhere on them that would hold. Some newer cabinet lines also have that, like most of Masterbrand's lines, but not KM. They have a hanging rail that is designed to accept the screws to attach the cabinet to the wall. All attachments must go through the rail with good meat around it, and hit as much of the stud as possible.

Any reason why a cleat won't work?
Just asking. I really don't know if it's feasible.

A clean is no possible really unless there is a certain skill set on board to be able to do some actual carpentry work. I'm sure you've developed the skills CEF. Not so sure about the OP. But really, it's not needed if the cabs are hung properly. A hanging rail with a single screw is more than strong enough to support a cabinet if it's attached to the adjacent cabinets. And they are attached properly. It's the "properly" that is causing the pause here.

Excellent advice.

Or, you could open up the wall, notch the studs and add 1 x 4 strapping.

Or securely screw 1/2, 5/8 or 3/4 inch to the wall and install the cabs over that. Any exposed plywood edges would need to be trimmed out.

Either way you won't have to hope to hit a stud when you go to hang the cabs.

Once when faced by an excessively "critical" client, I sucked a truss head cabinet screw 1" into a ceiling joist, hooked my claw hammer over the head and started doing pull-ups, after the 3rd she said OK,OK, I get it.

The "critique" stopped and the project continued smoothly.

I weigh 200lbs.

I'm mostly impressed that snoonyb can do pull-ups from a hanging hammer.....

Thanks, some good advice today. I already did one room and I can assure that my 10K of cabs looks like 10K of cabs. This is my not my first time hanging cabs. But it is the first time the studs wouldn't line up. I'm sure I am being paranoid about support since the old cabs were much heavier, only one screw and a short one at that.
I like the advice about installing support attached to the studs to screw into. It won't make too much of a mess.

If these are regular faceframe cabinets, you can "let in" a flat 1x4 across the top of the 3 cabinets and very securely link them all together, and install as one bloc. You can notch the very top part of the cabinet sides so the 1x4 is flush if need be, and this form of mortise if done well gives a lot of rigidity to the connections. Then the two flankers will be able to carry the extra weight without becoming warped.
Casey

" weedyacres"

It was a 32oz., knurled head vaughn, drilled and leaded.

Only one stud to hang heavy cabinet????

I'm so sorry but I have to ask -

Does he not have a friend?

I just couldn't help it. Sometimes a little humor helps to lighten the mood.

Aw, you stole my line vwhippiechick - that's the first thing I thought of when I saw the subject!

I developed a serious appreciation for the holding power of screws in a similar way to snoonyb. I was taking down a recessed light fixture which I thought was nailed in. After yanking and pulling and literally hanging and bouncing from the end of a pry bar trying to pry the damn thing out, I finally realized it was screwed in. Duh.

it's looking good. I cut out two pieces of drywall last night that will allow me to span two studs (jokes are welcome; I wonder if plumbers still see the humor when people talk about nipples). I will glue and screw in 5/8" plywood that will provide a second position to attach the middle cab.
I do plant to connect the three cabs together before they are mounted.