Alright!
So I have a couple ideas on how we could possibly do this. Do tell me your thoughts on the matter!

1) The Usual Way - We will create the tamer, and we will decide on our digimon. Obviously this means each player has two characters. The human and digimon should be equally defined individuals with their own thoughts and ideas, even if they agree on almost everything. To do anything otherwise would go against the point of having a sentient partner. 

2) The Usual Way Revised - So we will each create our tamer, but you will talk with one other player who will play your digimon. Every player still has two characters, but this increases the interaction and leads to better fleshes out characters for both digimon and tamers. And if we're separated it ensures no single player is writing on their own, unless the situation calls for it. It takes a bit more trust and responsibility. 

3) Frontier - Much like the fourth digimon series we are off to collect the legendary spirits. This is pretty self explanatory. The downside is it because more like a battle shounen than an adventure and what have you and each character might not get an ultimate form. The upside is we get to focus on a single character. I loved Frontier and the idea, buuuuuuut well you know.

4) We become the digimon -  Pick a digimon and a digivolution line. The idea is very much in the vain of Pokemon Mystery dungeon. You wake up in the digital world in a digimon body. You're choice of course, unless you'd prefer somebody else chooses for you. 

5) Digimon World - We'll treat it a bit like a game. You can collect other digimon, and they'll be more along the lines of pokemon, but you can focus on completing missions for other digimon or humans. Be a part of a guild. Personally, this is my least favorite. You're delegating digimon to roles akin to that of pets or machinery but they still have personalities and thoughts of their own.