Actually, most boards that support Quad channel also support Triple channel, but it just doesn't make much sense to run them that way plus there are really no manufacturers selling three DIMM kits, and haven't been for a long time, so you either buy a four DIMM kit and don't use one stick, use all four sticks and have some extra running hopefully in FLEX mode, or buy three separate sticks to run together and hope they will play nice, none of the three options is very much recommended. Better to simply run quad channel with a four DIMM kit, or stick to a consumer platform and run pairs or quads in dual channel.
Most, and probably all, X79, X99 and X299 motherboards support dual, triple and quad channel operation depending on the population and number of DIMMs installed.
For AMD HEDT and server products, I'm pretty sure it's somewhat similar but I haven't worked with anything on the higher end AMD platforms for quite a long time. Regardless, it's probably not relevant to this conversation anyhow unless the OP is planning to spend several thousand dollars and I don't think that is likely.
And, Jaquith, who was probably one of the top three people EVER on this forum when it came to memory, as well as what I know from past work and a quick check to make sure I'm right, seems to indicate that there is not and has never been an LGA 775 supported chipset that had triple channel memory support. Dual and quad channel only.
https://forums.tomshardware.com/thr...r3-core-2-duo-motherboard.423055/post-4007873