When focussing with the D3200, is it possible to select more than one focus point? If so, how?
You cannot choose multiple points to have in focus at the same time in a shot.
You can let the camera choose which one of several points it will use as a focus point in the shot, but the camera will not make any attempt to get all the points in focus - just one.
You have limited control over how much of a scene around a selected single focus point will be in focus. To do this you control Depth Of Field mainly by selecting aperture.
It is not always possible to get everything you want in focus within the constraints imposed by available light or because you must balance between wanting a small depth of field for compositional reasons and needing a large depth of field for focus reasons. It takes time and practice to learn to find a good balance between these conflicting requirements when shooting.
As pointed by StephenG, you cannot always in a single shot focus on multiple different points, especially if they are at significantly different distances from the camera. You can adjust depth of field (with the associated drawbacks to maintain exposure), but this has its limits.
What you can do, however, is take multiple pictures of the same scene, with the focus set on each of the points of interest. You can then (try to) assemble the different pictures in post production.
There are two approaches to this:
simply use your favourite photo editing tool to assemble the pictures, taking good care of the transitions between them
or use "focus stacking" software that will (try to) do this automatically for you, giving you a much larger depth of field. You'll find a list of such software in the linked Wikipedia page, there may be others.
Note that changing the focus not only changes which points are in focus or not (blurred), it can also (slightly) change the relative sizes of the different objects, so this can make the operation quite challenging.
Also, I believe most focus stacking software is more geared towards assembling images with a range of consecutive focus settings rather than more extensive focus changes (e.g. a person at 1 m from the camera and a background several dozens meters away), but I might be wrong.