Houseful, If they go over the old stucco, not only will you never see what damage and leaks etc might need to be repaired - well maybe in theory the new stucco will protect it - your walls are going to get really thick. You might need to replace or extend window sills/flashings etc, since if they become recessed in the stucco, water will get behind them. Not good. I think the only way to get a satisfactory result would be to remove old stucco. I've done it, not fun. Mind you I dislike stucco from that point of view anyway :) Just because these guys SAY they can do it that way, doesn't make it so. Ask to see previous examples of this redo, and ask the owners how it's held up.

There is probably a better forum, but I will comment on the idea of an arch over the middle window. I don't see how an arch fits with it. It would look contrived and out of place for there to be an arch when there is nothing that corresponds or fits with it. Nor does it look like a house that has any kind of arch theme going on. Stucco trim that fits with the existing features will look better.

Just curious - how do you know there is stone under the stucco? Do you know of any source of old photos - original family still around etc? Are the other houses in n'hood same stone laid in same pattern as your foundation? Does the same pattern extend from foundation up to rest of their houses? If so, then a good guess would be your walls look like your foundation. Still.... you really dont know til you take it down (where have I read that before LOL). Is there an out of the way place (maybe in back or side ) where you could remove stucco to see what's there? Youd have to budget for putting stucco back on if you didnt like it. Otherwise I would budget for repointing, stone cleaning, and possibly some repairs before removing the rest of it - just in case you need to do it. Depending on size of house, it might not cost all that much relative to what other people pay for exterior finishes (eg new siding, even repainting a wood house costs many thousands of $$) If it was protected for 100 yrs it might be pristine. Or if water got back there then there could be damage from decades of freeze-thaw cycle- you just dont know. Finally, its possible it was always stucco which can be a wonderful natural finish itself. Look into mineral based paints for masonry - they come in a wide range of natural stone colors (as well as can be mixed to match any paint color) and form a chemical bond vs. being a plastic that sits on surface. Ive not yet used some on my masonry (winter came) but Ive been told they give a beautiful vibrant natural color,d ue to the fact that the colorants are minerals vs. chemical colorants. Limeworks and Keim USA are 2 usa sources (both have excellent customer service btw). Keep us posted!

FWIW that hasn't been our experience in Northern CA--paint jobs on stucco that has direct exposure to sun and heat don't last anywhere close to 20 years. (We got 15 out of our last paint job but that was with a few years where it was in absolutely appalling shape, but where we were about to do renovations that would then need to be painted so we held off--and we had already repainted the south-facing side once in that time frame.) Obviously Southern CA is dryer in the winter and gets hotter in the summer than Northern CA and maybe that helps extend the life of paint, but the issues with paint longevity here seem to be heat/sun related, not moisture related. General rule of thumb in our area is about ten years for a quality paint job (though just about everyone pushes it past that point and just deals with the fading/peeling paint!) I would find out how much more colored stucco is than a straight re-stucco, and decide accordingly. You can always paint it later, but if you start off painting, you're committing to that route for the long haul.