If you're playing minecraft on a PlayStation, and you want to play two different accounts on the same PlayStation during multiplayer, how would you do that? So same PlayStation, two different accounts, at the same time, during multiplayer. Does that make sense?
If you mean playing split screen I have the answer.
First you will need to make sure you are using a HDMI cable to connect your PS3 to your monitor (not sure why this was required). Once you have done this, load up Minecraft with your main account. Once Minecraft has loaded, turn on the second controller and log in as a different account (you may be able to do this with the same account). As your main account start the world you want to play on, once everything has loaded, a pop up will show in the middle of the screen saying something like 'Press start to play splitscreen' or 'Press the pause button to add account'. Once you do what the pop up says the game should hopefully change to split screen.
PS. I am telling you this from memory back when I did this on xbox 360. If this didn't work, search 'how to play split screen on Minecraft PS3 edition' on YouTube. Doing this worked for me back when I did this.