A full chromatic electronic tuner and patient experimentation should help to understand the causes. You don't have to buy one, there are a couple on freeware sites (or were, I haven't looked lately) which work well with a computer, when you use a good microphone.
My guitar is the same, and that is because I built a new bridge and tuned it by ear. The neck angle was too low so I needed a lower bridge, and I got the bridge ALMOST right. OK with barred chords, horrid with a capotasto.

A friend made a bridge bone for his box that was thicker than normal at the base, and shaved sideways at the top to lengthen and shorten strings. A lot of fiddly work, but it fixed the problem. He has to be careful of the order in which he changes strings, though.