There's several options depending on the system you're using (Single Stage or Two Stage), but the classiest way to do multiple colors is to go with the Two Stage system using base and clear coats.
Base coats can be taped after very short drying times so what you would do is to spray the base color, then lay out and spray the stripe colors (still using base coat). You should be able to do the whole process in a day easily.
Then with all the base colors on, take off every bit of stripe tape and clear coat the whole thing. The clear will smooth out the color transition areas.
Do NOT under any circumstance do any sanding of the base coats during the process. Clean the base coats with a wax and grease remover (such as PPG DX330) and wipe dry with clean towels, and then use a tack cloth to pick up any dust. But do NOT sand any of the base coats before clear coating.
The fewer number of colors you use, the easier this is. If you like fogging and ribbons and all that stuff, the same applies. Do all the color with the base coats and clear it all together.
If you're a newbie to this sort of stuff, it's possible that you'll build up a bit of dry overspray while doing the base coats, but don't sand it off before clearing. If you aren't happy with the result (textured finish due to overspray under the clear), you'll want to let the finish dry, lightly wet sand with something like 1200 grit sandpaper, then clear it again (make sure you don't sand through the original clear).
Now's the time to rethink that super custom, multi color, ribboned, checkered, color scheme
Also remember that the more colors you use, the more tedius it will be to repair those areas later when you get an ouchy that you can't live with.