Just in a splice box? No, don't do that. You'll burn the house down.
First, assess the main panelboard. If that's OK, and up to the load (I'm betting that it isn't), you could install a subpanel in an upstairs closet, and run branch circuits to the upstairs rooms off of that.
But my real recommendation is for you to hire a licensed electrician to evaluate your current electrical system.
I agree with hiring an electrician. In my state you need to pull a permit for major rewiring like this and have a licensed electrician sign off on it.
I'm planning on updating the wiring in my new (old) house. What we have now is armored 15 or 16 gauge wires (with no ground wire of course). The whole upstairs is on one circuit, which is fine for lighting, but I'm uncomfortable putting heavy loads on that kind of wiring, like the multiple window A/C units we need. My plan is to run a 10 or 12 gauge line up from the basement, then probably regular 14 to the rooms.
My question is, how do I break into the armored cable? Is it a code violation to run regular romex back through the armor, or do I have to start over and fish a new run?
