Stacking lenses for higher magnification (a DIY microscope) Recently, I have made a DIY microscope stand for my phone according to these specifications.
I am using a lens that I found in home, the closest match that I could find is here.
I got some great pictures using this build, but I wish I could get pictures with higher magnification. 
Is it possible to stack lenses to get better magnification? If so, how should I align and space them for best results?
 A: Yes, it is possible, up to a point. As the magnification goes up, so will the image errors. The more magnification you want, the harder it is to build a good lens. Scientists in the 19th century were struggling with the problem of how to improve the quality of their microscopes until a German named Ernst Abbe figured out the theory to design next to ideal optical lenses for this purpose. 
The theory is quite complicated and you really don't need it at this level. The short story, at least for your purposes, is that, in order to achieve more magnification with small errors, several lenses are needed. Each lens should only change the direction of the rays coming from the sample by the smallest possible amount.
You can see a very typical minimal microscope here:

The important part is that the front of the first objective lens is flat or almost flat. That's called a plano-convex lens. By placing the flat (in German "plan") side towards the sample, the first refraction occurs at a smaller angle between the rays and the surface of the glass than it would if you had a lens that is convex (bulging out) on both sides. This principle can be repeated multiple times inside a good objective lens, like shown here in (a), where the first two lenses are plano-convex ones:

It is likely that most lenses you will find at home are symmetric convex on both sides. If you have several of these lenses, pick the one with the longest focal length (that's the one with the least curvature) to be closest to your sample, then the one with the second longest and so on. While this is just a rough guess, it is likely that this will give the best results for your purpose. If you are lucky and you can find a plano-convex lens, then you can do even better.
