I know that indirect commensalism and apparent competition are possible, but is indirect mutualism possible? Is there a way for two organisms to benefit one another through the use of a third?
If I have understood you well you're asking for a relationship in which the "third" organism has no significant effect on the mayor exchange between the two agents of the mutualism.
If that's the case I think that a good example could be something like the system of anemone and clown fishes in coral reefs. In this relationship the coral reefs has structural functions, supporting the anemone community.
If that's not the case and the third part can have a mayor role in the relationship the best example would be some kind of parasitism as the one noted above by Mason Heiserman in which the third part has a trophic function.
I think you are referring to facilitation, as Dr Young mentions. By the way; I like a lot these papers, Todd Palmer taught me Community Ecology in my PhD program. The book and papers of Judith Bronstein are very good to get you in this topic, here is one http://userwww.sfsu.edu/parker/bio840/pdfs/2013/Bronstein2009.pdf . In my dissertation, I found out that hummingbirds and flowerpiercers benefit one another through the use of some flowers
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