Is there any value in ultrasonically cleaning a record multiple times?

Not unless it wasn't cleaned properly the first time. 
Listen to it after one cleaning, then again after more cleanings. 

One cleaning is enough unless the record was exposed to things like cigarette smoke or cooking fumes which are more stubborn to get off. The addition of alcohol at 1% helps in that regard. Record that are clean, stored properly and played properly will not have to be cleaned again except for a sweep to remove incidental dust.

Yeah, that is what I was getting at, records that haven't exactly been taken proper care of in the past. Ok, I will try that. Thanks

I actually A/B tested this out of curiosity. 
I filled my tank half way with Distilled H2O, alcohol, some photo flo, and a dab of surfactant and cleaned both a fairly dirty record and a fairly clean record once each so that only the outer halves of the vinyl were in the bath. I listened and - with both - it was like a wall of dirt hitting my ears when the clean part was “over.” More-so with the dirty one, but the point is you could tell on BOTH where the line fell. I then filled the bath fully, cleaned them both again so that the first half was twice-cleaned and the second half now only once. On second listening I could definitely hear again where the second cleaning ended and the single-clean began. It was not as “drastic” a change with the second bath with the cleaner record, but it definitely helped to clean them twice. I imagine diminishing returns takes over after that... 

Ultrasonic machines are certainly very good at well cleaning a record. However, IMO, the best way to clean a record is by using the Keith Monks RCM. It uses a surfactant solution brushed into the record spinning on a TT-like platter and then completely vacuums of the fluid with a German medical grade pump attached to a TT-like arm that goes over the disc one grove at a time.
This is the machine used by the Library of Congress, the BBC, Better Records and many others for several decades.
And the cleaning process only takes about a minute per side instead of 10+ minutes.