For me, the single best way to re-roof a house is to remove the old roof first.

Yes, technically, you can put a new roof on over an old roof, but - why would you want to.  (Three roofs are totally out of the question).

If you have leaking in your current roof it is definitely time for action.  Leaking leads to rotten wood in the roof decking which can lead to nothing but trouble if you cover it up with a new roof.

In fact, if you have any unresolved leaking issues you should definitely tear off the old and replace it.  Adding a new roof over an existing leaky roof will only exasperate the problem.

You will also find some shingle manufacturers that will not warranty their product when installed over an existing roof.

You will also have to disclose the double roof at re-sale, which could possibly end up costing you money at that time.

Think of it this way - why would you want to spend a good chunk of change and not get a complete job?

Take it off.  Take it all off.