they are 2 different leagues, and no im afraid you cant do it alone
here are the difference :
The Moshpit Series will be used as a league that will rotate around Team deathmatch and other objective modes, the mode will use standard rulesets. This means that this league will comprise of a playlist of modes that relate to the public rulesets. The Moshpit series will be best for casual players and those players that are used to the standard match rules that have been used throughout the Call of Duty series. All the games in the Moshpit series will comprise of a maximum of 12 players, meaning that the games will be 6v6. The ranking system will be that of a solo rank,which will mean you will rank up as an individual player.
The Championship Series will be played as a mix of objective modes only, these objective modes will be based around a competitive ruleset. The competitive series will allow for team and solo rank. All games in the Champions series will comprise of a maximum of 8 players, this will mean that all games will be 4v4. You can rank up with you team mates in your clan or as an individual, similar to a pick ups game.
To receive a rank in one of the series, you will be required to play 5 placement matches before hand. That means that each series requires you to play 5 matches. Once these 5 matches are completed you will be given a ranking that relates to the series that you are participating in. Here are all the ranks that are achievable in Call of Duty as a single player or as a team: