Combining multiple power sources
Yes, of course it is. This is how national grid systems work - multiple generators all feeding into one grid - and how battery banks are made up of series and parallel connections of batteries.

If by "power supplies" you mean mains-powered DC power supplies then these too can be series and parallel connected provided that they are designed to do so.


  Is it possible to combine the power of two power supplies to increase the total current and voltage?


Given two identical power supplies designed to be series or parallel connected then you can series them for double voltage at the same current or parallel them for double current at the same voltage.