Think about the literal meaning of "aguentar": to have enough strength to carry, to lift, or to keep a weight lifted.
So, it's easy to see two forms of "take" in this case.
1 - Can't take/stand it any longer.
2 - Can't take any additional weight or task.
In both cases, they are pushed to their limits.
If you would translate "they don't take anymore" (then it's not about being able to do something, but just not doing it), it would be: "eles não pegam mais" or "eles não aceitam mais".
If you are looking for an English word, think of "withstand" or "bear". You are talking about the ability to bear a burden, It is usually about putting up with something negative: pain, abuse, exploitation, infidelity, etc. You could say "I can't take anymore laughter" but most of the time what you complain about is negative.
"They can take it no more"