Bittering: In creating an "imperial" or "double" or whatever version, you should consider how the increased alcohol and almost certainly increased residual sweetness and body (higher FG) will require more balance from hops. A good guide would be to think about the BU:GU (that is, IBUs/OG) ratio of the base beer, but also think about the ratio between the IBUs and the FG of the base beer. If you're scaling a recipe up, the BU:FG measure may be a better way to think about the balance between bitterness and sweetness in the doubled beer. So calculate your expected FG (which requires you to know something about what yeast or yeasts you're using).
Flavor and aroma I think depend heavily on the style you're going after. Very strong beers often benefit from (or even require) aging, and hop character--but especially aroma--will decrease quickly with time. So if you want to achieve an end product that will have hop character after, say, three or six months, you will need a lot of hops. The same goes for bitterness too--a beer aged for six months to a year will have lower bitterness than at one month. So think about how long you're planning to let it age. (This is less of a concern for IPAs, since you're usually going to drink them young--otherwise you lose the hop character. But some English IPAs are supposed to sit for a while.)
The one nice thing about strong beers is that they can be more forgiving. You have a lot of flavor and complexity to hide behind, so a difference of a few IBUs or a missing or additional 5 minute hop addition won't make or break the beer the way it could with a smaller, delicate one. So you shouldn't worry about experimenting. (Of course, you may have to wait months before you know the real result of your experiment, too!)