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Create a tournament with Swiss system

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In theory, yes something like this should be possible. Set the competitions first stage as a cup stage. Have every team play in the first round (round 0) (sort teams by reputation or random or however you want). Set the index of next round for winner to "1" for the next round. Set the index of next round for loser to "2" for the round after. Then for rounds 1 & 2 have half the number of teams from round 0. Repeat this for the next few stages. For round 1 (the winners from round 0) set the index of next round for winner to "3" and the index of loser to "4" and again have half the number of teams from rounds 1 & 2. Do the same for round 2 (the losers from round 0).

By doing this you can have a competition with multiple rounds pairing teams with identical win/loss records up to that round. The total number of games a team will play will depend on the total number of teams. An 8 team tournament would see all teams playing three games but a 128 team tournament would see teams playing seven games. Basically each round a team plays halves the number of teams from their previous round until there are only two teams remaining in the round. For example the 128 team scenario would have 64 separate rounds for each team's final match. Therefore, although technically possible, this probably wouldn't be much fun to try and create in the editor.

The important final step is to create a 2nd stage, this time as a league getting every team in the competition entered into it. Have this stage create no fixtures (untick "create fixtures" on the "league settings" tab. Then go back to stage 0 and on the general tab "process results into stage 1". This will mean that every result in the cup rounds will update the league table, making it possible to see every team in the competition ranked from 1st to last.

Hope this helps you create something similar to what you're looking for.

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