Its an interesting question but there's no easy answer.
This is extremely simplified but... you can theoretically get charged with a separate count for each victim affected or each separate time the offense occurred in its own transaction.
For multiple victims picture buying a keg of alcohol for your minor neighbor. That is the crime of purchasing/furnishing alcohol to a minor. But if you invite over 9 of his minor friends, you've now got 10 counts of the same crime.
For separate incidents, imagine throwing one of these parties in January and then another one in February. You could theoretically have 10 counts arising out of each. But if the two parties are too close in time to one another it could be considered the same criminal episode and would just be a single count, or in this case a single group of 10 counts.
But as I said, this is overly simplified. Some statutes regulate how multiple counts can be filed. For instance in many jurisdictions a simple DWI becomes a felony if there is a child passenger. In such cases, the child is listed as the "victim" of the crime. Yet in some jurisdictions you can be charged with multiple counts if there are multiple children in the car, while in other jurisdictions you can have a whole litter in the car and its still just one count of DWI with child passenger.
Finally, the State may always elect to proceed on just some counts for various reasons. Imagine you've got prolonged sexual abuse of a child. There might be 30 individual transactions of the same offense, but they all kinda blend into the same 5 year period. You wouldn't want to charge each transaction separately because then you've got to prove each one, including the specific date it happened, individually. Its better to just charge the one count and use all instances as evidence of the defendant's intent to commit the crime once. Then the jury must just believe it happened at some point over those 5 years. They don't have to be unanimous on which specific occasion it occurred. (there are exceptions to this too though for crimes against specific conduct. Like I said, there's no easy answer.)
Finally, the State has to be practical about charging crimes. They look like schmucks if they charge somebody with 20 counts of what are fundamentally the same offense. The bottom line is that the sentence is going to run concurrently if the counts are tried together so it doesn't matter how many counts they are convicted of, the jury is still going to take the whole story into consideration and sentence them to X number of years in jail or on probation. And the Defendant always has the right to be tried separately on each count which, though usually highly prejudicial to the Defendant, means the state now has to try the same Defendant over and over again.
Most of the time that you hear about people getting charged with many many counts, its Federal prosecution and they're trying to make an example of the person.