more power from both sockets?

To add to Elizabeth's post: If I were worried about the available current at the wall, I would (hire an electrician if you do not know how) check all of the series connections of that socket back to the box. You'd be amazed at how poor some of those connections may be. Re strip the wire and make sure it is using the screw connection, not the push in holes.

Just to gain more insight to this question, would it be advantageous to have a separate dedicated line to each component?

I like to have one dedicated line reserved for the amp, a second for the front end, and a third for digital.

Just to gain more insight to this question, would it be advantageous to have a separate dedicated line to each component?

If your components use three pin AC plugs, that's perhaps the worst thing you could do. It only makes ground loop issues worse.