There could be as many pathogens as there are types of self-replicating organisms or molecules.
Bacteria and eukaryotes are earth organisms. Other planets would likely have radically different organisms, any of which could be a pathogen. Both single-celled and multi-celled organisms can act as pathogens here on Earth, so alien single-celled and multi-celled organisms (or even organisms that lack anything we could identify as a cell) could be pathogens.
It wouldn't have to be a full organism, any self-replicating molecule could be a pathogen, as long as it can successfully enter the body and find the raw materials to replicate inside. This could include molecules not found on Earth. It can also include molecules that are found on Earth that have the potential to self-replicate, but don't currently self-replicate on Earth, such as RNA or DNA (there are "naked" RNA pathogens, viroids, but they use a cell's replication machinery rather than replicating themselves, and in the cell RNA and DNA need other molecules to replicate). Similarly, prions work by causing other proteins to mis-fold into more prions. But RNA and DNA also fold in important ways, so there is a potential for RNA or DNA equivalents of prions to exist (although as far as I am aware none are known).
Finally, from what I have found there is one (and only one) group of organisms on Earth for which no known pathogenic forms exist: archae. However, archae are particularly hardy, often living in extreme environments. This could make pathogenic archae hard to defeat with our natural defenses or medicine.