Ok, posted a bit about this yesterday, decided to come back with some more concrete stuff.

So, I've been playing Moon, and I decided I wanted to try and do a team based around all four weather effects. I get that this might not be the best choice competitively, but it sounds really interesting. So, I've gotten this so far.

Mamoswine
Thick Fat
Hail
Ice Shard
Earthquake
Avalanche

Tyranitar
Sand Stream
Fire Punch
Earthquake
Crunch
Stealth Rock

Shiinotic
Rain Dish
Sap Strength
Sunny Day
Moon Blast
Giga Drain

Trevenant
Harvest
Substitution
Horn Leech
Shadow Claw
Growth

Lapras
Hydration
Rest
Blizzard
Rain Dance
Surf
IVs: HP, SPD, DEF

Relicanth
Swift Swim
Rock Head
Waterfall
Rock Polish
Rock Tomb

Idea is for most of the team to either take advantage or at least tolerate multiple weather conditions. The main combos are Trevenant's Sunny day setup for sweeping and Lapras's stalling with rain and rest. However, a lot of the rest of the team does some interesting stuff as well. Relicanth can use Rain to become a pretty decent bruiser with his speed, while a sandstorm makes him pretty defensive. Shiinotic serves to set up Sun, but enjoys Rain for helping him with his healing. Lapras can use Hail to murder with Blizzard, and Mamoswine doesn't mind being in a sandstorm.

I'm still heavily considering swapping Shiinotic for Whimsicott. Whimsicott is faster and can use Chlorophyll to hit pretty hard in Sunny weather. It's mostly finding out is Sap Strength is worth it for dealing with super physical Pokemon.

It's also worth noting that I'm basically unaware of the meta or higher level strategy in this game, so if I've made any serious errors(beyond, you know, the basic team concept, I get that one), I'm certainly welcome to critique.