合える is the Potential conjugation of 合う。
Attaching ~ 合う （あう）to the end of a verb stem means to do the action with each other or to do the action mutually with someone else.
(See more examples on the source page)
Attaching 〜合う and 〜合える in this way is pretty common.
To determine whether it would be fitting in a certain situation, a good rule of thumb is to ask “Is the verb something you do to or amongst each other?”
I advise against “with each other”, because for example you don't say 「泳{およ}ぎ合う」 to mean “swim with each other”. (In the rare case that it is used, it means more like “swim amongst each other” as if intermingling.)
A few combinations will need special attention as they have a counterintuitive meaning:
落{お}ち合う
Does not mean “drop each other”, but to “meet up”.
Added:
A Japanese friend who is more knowledgeable than me in grammatical terms told me that what I wanted to say in the “rule of thumb” section is better summed up as: “whether the verb is intransitive (自動詞) or transitive (他動詞)”. 〜合う is only attached to transitive verbs.
A great example they gave was the verb fly, which can be both intransitive (飛{と}ぶ) and transitive (飛ばす). This explains why you generally don't say 「飛び合う」, but you can say 「飛ばし合う」.
