This will, of course, depend on the specifics of the class and how your institution allows it. At mine, one set of classes in the applied mathematics department was Multivariable Calculus (also known as Calculus III) and Differential Equations (Calculus IV). Although the former seems to be a prerequisite for the latter, this is actually not the case; I took the latter before the former, and some students have actually taken them concurrently. Now, it should be noted that there is not so much overlap between the two classes they way they are taught at my institution, and it might be different at other institutions.
However, some classes are listed as prerequisites before taking other classes because they contain information or material which are a foundation for later classes (where you are expected to know the material taught in the prerequisite class), and even if you were able, you would be doing yourself a disservice to cut corners like this. In the case of language classes like Spanish, it wouldn't be so smart to try and take Spanish II without knowing the material of Spanish I. I would probably take Spanish I for a refresher or see if you can transfer credit in to bypass it, it doesn't seem to make sense to take both of them concurrently.
Again, this depends on how your institution sets its policies for prerequisites. First, of course, ask your advisor for advice on this and consult the official course catalog/bulletin, since it should list classes, policies, prerequisites, etc. If you feel you should be able to take Spanish II, consult the professor teaching that class and get input from them as to whether it would be a good move or not.
Hope this helps.