This question comes up more often than most homeowners might imagine. The simple answer is, yes, of course. The real question becomes do you need to have different sized cabinets and, if you do, will they look awkward? If you're asking yourself this question, it's probably because your gut is already telling you it won't look as nice as a more uniform cabinet arrangement. The first thing to do is to figure out what would have to happen to reconfigure or replace your cabinets and, then, get an estimate. If this turns out to be implausible, you need to reevaluate the appearance of different sized cabinets and, possibly, consult a kitchen decorator/organizer to ensure you're aware of all your options.
Soffits and Structural Beams
There can be many reasons why existing cabinetry can't be moved or modified, but many of them are not nearly as difficult to navigate as homeowners think. Many cabinets, for example, have a soffit that covers a structural, support beam. A contractor can use temporary support beams and the existing beam can be removed. By trimming the joists flush with the edges, a new beam can be installed that's long enough to rest on the wall or post. This will free up that much needed ceiling space for your cabinets. It sounds daunting, but it hardly counts as major construction and is probably a lot cheaper than you think.
With your new space you can move your existing cabinets to make them work better with new cabinets or you can completely replace your kitchen cabinetry. You may have been set on using your old cabinets, but when you realize the possibilities that are open to you, you may find yourself changing your mind.
If you don't have the money to make entirely new cabinetry plausible, but you're still concerned different-sized cabinets won't look right, consider if you need the cabinets at all. There's more than one way to store a pot. Hanging racks are an integral part of many a kitchen décor. A Tuscan style kitchen encourages you to store common cooking ingredients in openly visible jars. Hiring an interior decorator, if just for a two hour consultation, can help you decide if those cabinets are worth the aesthetic costs. This decorator will be able to give you advice on reorganizing your kitchen and give you an honest opinion about the appearance of different sized cabinets in your specific kitchen.
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Make an Informed Decision
Don't just give up and buy bulky cabinets without taking a close look at your options. Even moderate kitchen reorganization can free up enough space so your new cabinets can be small enough to match the old ones. If you talk to a kitchen remodeling contractor and an interior decorator, the overwhelming likelihood is that the answer is out there. It's even a good bet that you can add storage, increase the aesthetic value of your kitchen, and do it for a reasonable price.