Within mixed methods reseal (MMR), the phrase "multiple methods research" usually means several qualitative (or quantitative) methods used together, rather than a mixture of both qualitative and quantitative methods.
My own preference is to think of MMR as integrating the results of qualitative and quantitative methods, so to the extent that a case study produces both kinds of results, it certainly could be mixed methods. An alternative situation would be where one or the other kind of method was used in a purely descriptive sense, without producing any results that are relevant to the research question. Thus, simply collecting quantitative (or qualitative) data is not enough to make a study mixed methods.