Can I publish multiple papers with same methodology but different topics? I'm investigating differences in esophageal cancer incidence and mortality rates between my home state and the rest of the United States. There already exists a paper that performs this type of analysis for colo-rectal cancer using data from a pre-existing database (SEER).

If I used that original author's methodology (citing him of course) and gathered data from that same database, but adapted it towards investigating pontine cancer instead, would it be publishable, assuming my content is otherwise unique and competent?

If the former holds true, it there anything that could/would stop me from creating an indefinite number of research papers that are permutations of my original except with other cancers like lung, breast, skin, etc? Or even different states?

I don't want to do anything unprofessional or unethical here so I would like to know sooner rather than later. Please advice and thank you.
In general, the test for whether a result is publishable is whether it advances the state of human knowledge.  

Thus, if X is a new approach that contributes to knowledge about Problem 1, then it could readily be published in either a methodology-centric venue or a problem-centric venue.  If X is applied to produce new knowledge about Problem 2, then that's less interesting from a methodology perspective (though it may still be interesting, depending on circumstances), but absolutely relevant for Problem 2.

So if the approach really is useful for learning about lots of different types of cancer, it's potentially publishable for each type.  At some point, though, generalization becomes more interesting, and it would be appropriate to write a (much higher impact) paper on the applicability of the approach for learning about all cancers.