How many variables may be tested legitimately in any one experiment?

I think it's very difficult to answer this question simply. Depending on the sophistication of your research model and the amount of data and the accuracy with which the research is carried out, you can test several variables simultaneously. This can be done 'legitimately', and sometimes it is too costly to run research projects that test one or two variables at a time. Some of these complex and sophisticated statistical models are used very infrequently, but it can be done.