Make sure your choices look intentional. If you have 9 guests but only a setting for 8, don’t add just one odd setting from a different design of dinnerware. You want to develop a patterned dinnerware design so the table has an appealing style to it.
You can use different settings at the foot and head of the table. This is a straightforward pattern, and works pretty well if you have two patterned dinnerware sets which are a lot different from one another. Dining room sets will sometimes have different kinds of chairs at the table ends, so giving those seats the different patterned dinnerware would work well.
If you have different matching styles of dinnerware you can rotate the settings on the table. If your sets of dinnerware are different, you can give a smaller patterned dinnerware set to children if any are present. This type of pattern will look intentional, and the kids will be happy to have their own special patterned dinnerware set.
If you have complementary patterned dinnerware sets, you can alternate and combine at the same time to make for a very attractive patterned dinnerware arrangement. Unify the settings with any pieces you have enough of.
If you have completely different colors of china, like blue and pink, try to find place mats or a tablecloth or that integrate those colors in a pattern or print. White linens at each place setting may also help you coordinate the patterned dinnerware settings.
You also may want to consider decorative paper napkins and patterned paper plates for dessert. Using these, for a very low cost you can purchase all matching plates & napkins for any amount of guests. There are plenty of bright and beautiful prints to choose from that would work with formal or casual patterned dinnerware.
If you need to use more than one set of glassware or silverware, appoint them to a specific dinnerware set and use them for that set to keep the pattern consistent.
For really big dinner parties where an assortment of tables will be used and many different sets of patterned dinnerware will have to be used, you can use the above guidance for each table. Be imaginative and have fun.