Can an animal have more than one type of symbiotic relationship with one species? For example how humans can have a parasitic and mutual relationship with plants. Are there more like that?

Life is not like Dungeons and Dragons! There are no pre-determined rules that say what combination of character-classes or special powers are possible. Organisms will evolve the sybioses, parasitisms and mutual relationships that best propagate their genes, whether that means zero, one or many such relationships.