Splitting a circuit breaker into multiple lines
This seems to be relatively common especially with older homes.

If your basement is not finished then this might not be that large of a job.  If the basement is finished it makes this a lot harder and you will definitely be making holes in walls/ceilings.

The first thing you need to figure out is what exactly you are going to split. Most locations requires dedicated 20amp circuits to each recepticle in the kitchen, so instead of trying to break up a number of other circuits, it'd probably be easiest just to run new dedicated circuits for the kitchen. You do need to be aware that it is not always permissible to have multiple circuits running in the same electrical box, so you could probably make it even easier by running brand new outlets instead of trying to change existing ones. 

Installing a new breaker and outlet is not that difficult, but safety always comes to mind with electrical, so if you are not sure you could opt to have an electrician do the whole thing, or if you just want peice of mind, you could get them to inspect your work upon completion.

As always, make sure to turn the power off when working in your electrical panel.  I know a lot of people will pop in breakers with the power on, but I prefer to have my hands nowhere near live electricity.

Good luck!