This can be either directly or indirectly just a military conflict in which both the USSR and US were on the same side.
The short answer is yes.
The long answer is one I'm not qualified to give you, but the Biafran War (discussed by u/aquatermain) and the Iran-Iraq War ([Soviet side discussed here] (https://old.reddit.com/r/AskHistorians/comments/l5g77i/why_was_america_so_concerned_with_halting_the/gkw0xh7/) by u/Kochevnik81 and American side discussed here by u/ghostofherzl) are examples.