It depends on how much caffeine is in your cup. Rather than measuring the size of a cup, I would go by the amount of coffee, as in the weight of the beans, used to brew it. The actual amount of caffeine is not as easy to measure, and even for the same kind of beans, there is natural variation.
For a traditional Italian espresso, about 7g of coffee beans are extracted. For a third-wave double espresso, it's usually 18g or more.
In my opinion, 10x7g is a lot. 2x12g is more than enough for me.
caffeine extraction is largely a function of time in contact with water. Espresso is quite quick brew, so has less caffeine than other brewing methods (yes, there are plenty of other factors)
There is no realistic scenario where, no matter your extractions or bean selections, 6-10 shots of espresso a day is not an enormous amount of caffeine
A grande americano at Starbucks is a 16 oz drink with three shots of espresso. Have one in the morning and one in the afternoon and you are at six shots of espresso. That doesn't seem all that enormous to me.
75mg per shot = 450mg caffeine
That's a bit over the recommended limit of 400mg a day the Mayo Clinic, FDA, etc. recommend. Not sure it it qualifies as 'enormous' or not.
The amount of caffeine that humans require to live is 0 mg. So ...
Irrelevant to the question (How much is 'enormous'?).