We would like to add stacked cabinets on top of our existing frameless cabinets, but the cabinet maker I'm working with says they would look like an after thought because it would be very difficult to get the trim/side panels lined up properly. There is no way to put continuous trim panels up without disassembling the entire kitchen and we don't want to do that. Any suggestions?
What I believe what your cabinet-maker is getting at is that most stacked European-style cabinets (like you have, with no visible face frames) are incorporated into the same carcass as the lower-uppers, which makes it easy to line up all the doors and ensure they line up exactly; since you want to add a separate carcass above the existing one, getting the stacked doors to butt right against the existing upper doors will require a) removing the existing crown trim and b) exactly measuring and installing the new cabinets. Even a small discrepancy in the door width, for example, will be very obvious.
I haven't got the experience to back up this opinion, but I think a very skilled carpenter could probably build cabinets to fit the right dimensions on-site, and then send them to your cabinet-maker for finishing. That would be a very expensive process, though.
Alternatively, you might consider replacing the crown trim with a design element that provides some separation between the cabinet levels, but makes it look intentional. For example, these stacked cabinets have a ladder rail between them:
The face frames above are aligned to the cabinets below as well, but minor differences wouldn't be nearly as easy to spot. You don't need to actually put a ladder rail on, of course; just anything to break up the vertical lines and give your implementation some tolerance for error.
I think that what he is saying is that the blank side panels (i.e. to the left of the oven and on either side of the microwave) will not flow continuously into the new upper wall cabinets' side panels.
I think that you could get around this by replacing the existing crown molding with a flat molding to cover the joint line. Similar to Robert's answer, the more visual distraction you add the less obvious this disjoint will be.
Also, I don't see why you couldn't layer a full-length side panel over the existing side panels. You'd have a visible edge you'd have to dress up somehow, but this doesn't seem too difficult.
Honestly, what I think you have here is a contractor who just doesn't want to think outside the box. You should look for someone who does more than just throw up prebuilt kitchen cabinet boxes. Try to find a real carpenter who specializes in custom built-ins. (Obviously this type of tradesman would be more skilled and charge more than a kitchen installer.)