Technically this would be a "cluster" not a "supercomputer" which may help you in your search.
You certainly can do this using software such as Beowulf (for scientific processing) or Hadoop (for data processing). However, the only way I can think of making money from this sort of thing would be if you were to rent space out on the cluster, but then you would be trying to compete with companies such as Amazon Web Services and Microsoft Azure where you could also set up a cluster. If you could figure out pricing to make this competitive then it could certainly work though.
However, there is one tricky part you will need to figure out - Power and cooling. Having 220 machines sitting running at 100% load for hours/days on end is going to pull a lot of power and generate a lot of heat, you would need to be investing in proper power distribution and cooling systems - You'd struggle to have this in a standard home/office environment without these modifications.
If you think of the average machine maybe pulling 200w at full CPU load, you are looking at pulling 44kw of power - Imagine running 22 electric room heaters all together, that's the power and heat you'd be dealing with! You can rent space in proper datacenters which would have the power supplies and cooling to be able to handle this but it won't come cheap!