I think what you are asking for is "Multiple Mutualism". Normally,
Most of the known cases of multiple mutualism involve relationships in
which two of the partners are at the same organizational level—usually
two bacteria that might be interacting directly—but are both essential
for the survival of the host
— Entente cordiale: Multiple symbiosis illustrates the intricate interconnectivity of nature -Philip Hunter
For example, the glassy-winged sharpshooter (Homalodisca coagulata) primarily feeds on xylem-fluid which is low on organic nutrients…so it depends on 2 bacteria, Baumannia cicadellinicola and Sulcia muelleri. The sharpshooter provides these with raw carbon skeletons present in the xylem fluid, and those bacteria in return synthesizes vitamins, essential amino acids, etc. For more detailed study, see Wu et al, 2006.
However, there are also examples of three-way mutualistic symbioses in which all the partners are at different organizational levels. One known case involving a virus, a bacterium and an insect, see Moran NA, Degnan PH, Santos SR, Dunbar HE, Ochman H (2005) The players in a mutualistic symbiosis: insects, bacteria, viruses, and virulence genes. Proc Natl Acad Sci USA 102: 16919–16926
Anyway, the essence as stated by Andreas Brune, Professor of Biogeochemistry at the Max Planck Institute for Terrestrial Microbiology in Marburg, Germany:
Multiple symbiosis is probably more widespread than we think, especially in view of the symbiotic systems involving different organizational levels, for example between bacterium, nematode and insect, or bacterium, protozoan and insect.