I'm not sure that stands up to logic though (not that theres much logic in DnD)
A frightened creature has disadvantage on ability checks and cant move towards the source of its fear is within line of sight. But having a second source isnt imposing more disadvantage on the PCs condition - its just cutting off further move options. ie I think the condition should be from the victims persepctive not the creatures
ie theres really no value it making saves against all sources since once the save is failed the intensity of the effect doesnt change much.