Can I connect 2 power supplies into my computer?

A second power supply can still be connected to a power source on a wall but you have the following problems:

1: Your power supply must connect via an ATX connector to a motherboard to function properly with your computer's power button. Only a computer connected through the main 20 or 24-pin power connector to your motherboard can receive a "wake-up call" from the computer to complete a circuit, turning on the power supply with the power button. With a power supply connected to an outlet and no computer connection, you can only flip it off through the main switch in back of it.

2: Most computer cases have space for only one power supply. A power supply outside the case providing supplementary power would require an open case and you would have to expose the power supply to the outside environment, not to mention that last inconvenience from problem #1, which is that you can't switch it off using your computer's power button.

I advise you to get yourself a decent power supply overestimating the amount of power your computer is expected to consume. Let's say your computer should consume an estimate of 300 W. You can still get a 500-650 W power supply to outlast your computer's future demands. There are Molex 4-pin splitters available at certain computer shops if you need room for more peripherals, but that runs a risk since not all power supplies support this.