It clearly depends on the tourney, the level of the tourney and the availability of umpires....Many tournaments require League certified umpires and that can lead to a shortage of Umpires. I have done 4-5 games in a row before and as you can imagine it is just not optimal.
4th of July or any Holiday tournament are always a challenge, as umpires have a family life as well and availabity to do games can be less....therefore the games are covered by those who will stay....
As a Director of Umpires for some local tourneys, I try and not schedule any more than double headers for umpires...they get tired and can lose focus...
As an umpire who does tournaments, I prefer to work no more than 3 games in a day (but not back to back plates)....I just cant mantain the level of focus needed to do a good job for each game....I cant imagine doing 4-5 HS or college level games in one day and expecting to do be able to put the best product on the field...