Adding a third storey - insane, or feasible?

[Aspidistra]

For reasons which I won't bore you with (well, unless you want me to ) I'm exploring the idea of adding some extra rooms to our house. This is an old brick terrace house ("row house" I think you call them?) which was originally single storey, but has had the attic converted to an upstairs bedroom.

There's no garden. The only way to go is...up! Ideally, what I want to end up with is two storey's all the way along, and a single (large!) attic room on top of that, making 3 floors in total.

I've never renovated before. Is this crazy talk? The foundations are good, but obviously weren't intended to hold more than the original one floor of weight. Anyone ever done anything like this?