curious as to what specific steps could be taken to train a pup to submit to and possibly enjoy being vacuumed. Calves love it.

The idea being that the source of the hair is the dog, perhaps periodic vacuuming of the dog would be simpler than vacuuming of the house. Have a vacuum designed for livestock with a nozzle that does not grab skin.

Have tried to train several dogs and the cat over the years to accept this and never had any luck. Obviously going too fast or doing it wrong with inadeguate rewards.
(cat went BONKERS!)

Here's how I did it:

Start with the vacuum cleaner off. Just stroke the dog with the hose attachment as part of the regular grooming routine.

Separately, condition the dog to ignoring the sound of the vacuum running. With a new puppy, I just turn the vacuum on and leave it running in the middle of the room and walk away. I'll let it run for 20 minutes or so. After a while, (doing this every day for a week or so) the sound of the vacuum cleaner just becomes part of the "normal" noise in the house.

Then start putting it together. You have to ease up to actual full-on vacuuming of the dog's coat, because the suction from the brush attachment will be the new thing. So try turning the vac on, and stroke the dog with the back of the brush attachment--combining sound, stroke, but no suction yet. Then gradually introduce the sensation of the suction.

Long firm strokes are better accepted than short, poking sucks with the hose. And lots of cheese helps at first.

Luca, my GSD, especially loves being vacuumed. Every time I get the Dyson out he comes over wanting a beauty treatment.

Have you worked with the dog being calm and uninterested in the running vacuum (vacuuming the floor) first?

If not, then the vacuum turned off with treats on it, etc.?

The first step is not to apply it to the dog.

And you are right: IME, most dogs like (or love) it if they're conditioned to it slowly (some love it immediately, but to count on that is to court disaster that's harder to overcome).

Never mind!

Tracy's protocol is great!

Thank you- Tracy's protocol sounds terrific.
Pup was terrified of the vacuum , now he attacks the vacuum: I'll leave it running, motionless, for a few days, let it become a bore.
We have plenty of cheese!

I would leave it out, visible but not running, first.

My own protocol with dogs phobic about something (like a motorized wheelchair, a vacuum cleaner) is to have the item out and sitting there but not running.

When it has become boring not running, and it's turned on, the dog is a room away. You see where I'm going -- no step in the process causes the dog to go back to reacting.