Adding a second story and would like to increase the R value and air tightness.  The second Floor is all new construction, so I can use spray foam.  The first floor is intact and I would prefer not to touch the interior, so I would have to add rigid insulation to the outside.  I am concerned
about condensation. Any advise?  The existing wall is typical of the southeast, sheetrock, vapor barrier, R13 fiberglass, 1/2 plywood or fiberboard with waterproof exterior and 3/4 cedar siding.

What part of the southeast? How old is your house? Are you certain of the poly vapor barrier and its location?
Have you opened any of the walls and investigated their condition?

Raleigh, Durham area of NC.  The Poly is between the sheetrock and studs.  The house was built in the mid 1980s.  People in this area often add vinyl siding over there existing walls and put a layer of 1/4 rigid insulation between the new and old siding, not sure how air tight they make it     ( probably not very).  Haven't heard  of any problems with this.
 I am concerned that adding 2 inches of rigid foam and a exterior vapor barrier would create a similar situation that Dry-vit (stucco) applications had back in the 90s  (moisture that couldn't escape).  I have been into the walls and they are in very good shape.

In the Southeast in the 1980's we were encouraged to install the vapor barrier between the drywall and the studs.  I have designed and built this way with 2x6 studs.  Several homes including some of mine also used either 2" of Thermax or 2" of Styrofoam (blueboard) on the outside of the studs with 6" of fiberglass between the studs.  However, we never taped the seams in the board insulation like they did in Indiana.  So far I have not heard of any problems with this method.  I have kept in touch with some of my clients from back then and actually visited some of the homes to see how they were holding up.

Since you have a highly vapor-retardent layer on the interior you really HAVE to set it up as drying-toward exterior (which would be pretty lousy practice in FL, but should work OK in NC.)

If you use 2lb foam you would create vapor traps, and mold issues would be almost guaranteed after some period of time.

You could get away with half-pound foam, (~10 perms @ 5" thickness) but fiber-faced polyiso (not foil-faced) would have better drying capacity (over 25 perms @ 3") and higher R-value per inch of depth. The stuff us usually sold as roofing insulation in commercial building, but it should be just fine glued & long- screwed through exterior furring strips over your existing sheathing. With another layer of sheathing screwed to the same furring strips you get a good rainscreen gap as well (the felt or housewrap drain-plane material should be between the furring & iso), while preserving/enhancing the outward drying capacity. 3" of iso will give you a full-on R20, with none of the thermal bridging you'd get with spray-foamed furring or studs. It typically comes in thicnknesses starting a 1-1.5" up to 4-5". A 2" layer would add ~R12, more than doubling the R-value of a R13 f.g. insulated studwall, which performs to about R10-R11-ish with thermal bridging.

so... the final stackup ends up something like this:


(outside air)>siding|nailer sheathing|furring & gap|drain-plane|permeable isoboard|old sheathing|studwall & fiberglass|polyethylene|gypsum|paint<(interior air)

With the poly sheet, you have to take care than none of the layers between it an the outside are vapor-retardent or you're asking for trouble down the line. Foil-face iso, even un-taped could be problematic in time, especially if the siding is frequently weather-wetted. (If it has 2' roof overhangs and it's only 1 story tall you can get away with a lot more, but that isn't the case here.)

A couple of comments on the above stackup:

*The furring need to have sufficient fasteners to handle the weight & mechanical stresses of the new sheating & siding, which increases signficantly with insulation layer thickness.

**The new sheathing can probably be nailed insead of screwed. Some siding materials (like cedar siding) may not require nailing layer of new sheathing, and might be hailed directly on the furring.

***The the gap & drain-plane are key- allows both the siding & wall to dry quickly from weather wetting events, and reduces the vapor drive toward the interior that you would otherwise see in summer considerably.

Thanks Alton and Dana.  I'm considering both of your methods.  I like Altons for the simplicity and Danas for the greater R boost.  One question I have for Dana, when you say Sheathing nailer are you talking about an OSB or plywood? If so, are you purposely omitting felt or vapor barrier from their exterior?  My siding will be Stucco finish 4x8 sheet Hardie with a supporting 2x10 exterior band at each floor level.  Depending on how much thickness is added in Dana's method I  might have to add a thicker band.  As far as the second floor would you use 2x6 studs so that the upper and lower walls  have similar surface depth or just make up the difference with more rigid insulation?

Dana, You also didn't list my 3/4 inch cedar siding in the layers.  Are you recommending I remove it?

Dana, Are the gap and drain plains open at the bottom for air to flow.  In my case the furring strips and drain plain would sit on the band.  Do I need some type of air gap or vent to the outside?