In a strict sense, yes. Perhaps not exactly 80 but you could get close in a single administration of multiple high-valency vaccines.
Vaccines are designed to show your immune system pieces of things it needs to recognize and kill (called antigens). This allows your adaptive immune system to patiently work out antibody or receptor design (which can take between 5 and 20 days) without an active infection that is trying to kill you. This is generally considered desirable, as your innate immune system response is not as efficient. It's all the illness symptoms that you usually won't enjoy, and it fails relatively often; if the adaptive immune system takes too long and the innate immune system fails, this results in death.
Some vaccines have many different antigen pieces inside, from different viral lineages, because then your immune system gets to see lots of different things that it needs to kill. This is called valency. The standard flu vaccine used to be quadrivalent; it had pieces from four different flu viruses (two influenza A and two influenza Bs). Now it's trivalent, one of the influenza B strains got so beaten down by COVID restrictions that it's in danger of extinction (we briefly thought it was extinct but it's desperately hanging on), so we removed it from the standard vaccine. Other common vaccines (like the Pneumococcal Conjugate Vaccine) have even more different antigens. The PCV21 vaccine has 21 antigens.
Because these are separate antigens, you could administer them separately if you really wanted. The limitation would be administrative - the combined, high-valency vaccine is trialed and approved as a unit, and you would have to redo trials. This separability is distinct from an antigenic epitope, which is the specific part of an antigen that the immune system locks onto. Separating epitopes of an antigen into different shots is a much more difficult technical task, and you would expect that this technical work would yield candidates that fail as vaccines at a high rate. Saying that there are thousands or millions of vaccines in a shot because an antigen has many possible epitopes would not be correct.
Because these are separate antigens which could be reasonably easily delivered in separate shots, you could call this 21 vaccines in one shot. I wouldn't, but I wouldn't call it wrong, either. If my pediatrician described PCV21 as "21 vaccines put together to maximize protection" I would not object to that. If my pediatrician described high-valency vaccines as "just one burger with 10 choices of topping" or "one game with ten different modes or options" I would not find that acceptable (I'd probably get a new pediatrician; those analogies are entirely incorrect).
The implication of this claim is that these types of vaccine are bad. That there is a negative associated with combining many antigens into one shot. This is untrue; approved high-valency vaccines are trialed for safety and provide protection against a broader range of pathogens.
Your immune system is fighting far more than 80 things at a time to keep you alive. A large number of antigens in a single shot is not any more risky than fewer antigens, provided the combined shot has been trialed for safety and is carefully followed in post-approval surveillance (as all vaccines in the US are).
Providing broad coverage is a desirable attribute, and it is very reasonable that there are even higher valency vaccines in some stage of development or testing (the highest valency vaccine that I am aware of that has been approved is PCV23). A successful high-valency vaccine with 80 antigens that conferred broad protection against an entire bacterial or viral clade would be extremely beneficial, not a cause for concern.
"even beyond the actual [vaccine?/active agent?], they sometimes have 80 different [chemicals?/inert ingredients?] in them. It's crazy."He very often goes off on tangents mid-stream and rephrases things as he goes.