« Se soutenir » semble similaire mais je pense que « s’entraider » est mieux.

In English, we use the Latin phrase “quid pro quo,” which seems to capture at least partially the “mutual” notion of “s’entraider.” From the notion of that Latin phrase comes the expression in English: “Scratch my back and I’ll scratch yours,” which I’ve seen (never heard, though) translated as “Gratte mon dos et je gratterai le tien.”

I’m not sure if the French translation of “quid pro quo” as given in the above citation (i.e., “contrepartie”) captures the notion of “mutuality” as well as the original Latin phrase (or the “scratch my back…” phrase), and that’s why I would suggest either using the phrase in it’s original Latin (to sound more…?snobby?, for lack of a better word) or else the more familiar phrase “faire du troc” (or perhaps even the verb “troquer”), which does seem to capture the idea of “mutual exchange” and by extension “mutual aid.”

L’expression pour « aider quelqu’un » est « donner un coup de main » ; pour « s’entraider » on dit couramment « se serrer les coudes ».