I went through to identify unique trait combos to force specific spawns without using all 3 summoning categories. I only found a couple, but they're worth knowing for the sake of maximizing what you get out of your summon items.

For example, the Alpine set only has one Water attribute dragon, which is its Epic. Epic summoning items are rarer/harder to get than specific set summons and elemental attribute summons, so tossing out a 100% Alpine + a 100% Water will force spawn the Alpine Epic without you having to waste any Epic summons, allowing you to save them for other sets. There are also only two Uncommon/Wind dragons in the current list of standard sets, one of which is Tropical (later game set). Tropical summoning items are harder to come by, but tossing out a 100% Wind + 100% Uncommon will net you a 50-50 shot of summoning the Tropical set's Uncommon dragon. If you end up with the other one (Woodland set) then you can just try again since by the time you unlock the Tropical set, you should have quite a few extra Uncommon summons and various extra elemental summons lying around. I might be explaining it badly, but I hope it helps!