Is it possible to combine the power of two power supplies to increase the total current and voltage
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.
yes, this is possible.
e.g. it is possible two have some batteries connected in series or parallel, like here.
but if you have controlled voltage sources and put them in parallel to get a higher output current this can (or will lead) to instabillity as the different voltage sources will always measure a slightly different voltage and as an effect try to compensate the "error". So there has to be an additional communication and control between the controlled voltage sources so that there is stability.
Here you can read about one way to handle this.
The output of each power supply can be set separately. The output voltage controls of one power supply should be set to the desired output voltage (CV); the other power supplies should be set for a slightly higher output voltage. The supplies with the higher output voltage setting will provide constant current output, and will drop their output voltage until it equals the output of the CV supply.