I'm not american but have multiple copies of my own country's passport. I keep one 'clean' by not using it when I visit terrorist countries - ie cuba and anywhere that uses squiggly writing - and enter america on that one.
In the 70s and 80s it was trickier. If you had an Isreali entry stamp you couldn't go to any arabic country. I was even refused entry to Egypt once because some Egyptian immigration moron (they aren't all American) thought my Nepali trekking permit was Hebrew.
Similalry if you had a S African stamp you couldn't visit most african countries or anywhere describing itself as the 'democratic republic of'
South america was in theory tricky since every little tin pot dictator was always against every other little tin pot dictator but in practice their immigration was never organised enough to stop you
I work in mining and in the bad-old-days we used to have to keep multiple passports, to keep SAfrican, Isreali, Chilean etc entry stamps separate.
Now I tend to keep one passports just for the USA - it's easier than explaining to the TSA that visiting a country that doesn't speak English (like Jesus did) doesn't make one a terrorist.
Ironically the only problem I have had is that after being forced to get a brand new passport because the USA demanded RFID - I was questioned for 30mins on my lack of travel history!