As far as I know, the current system functions as the base rank, which determines the starting -RP as well as who you play with, +/- 1 rank from your own. You get through 4 tiers of the same rank to advance to the next. The starting RP, nor who you play with, changes within tiers.
This is objectively a faulty system, which especially penalizes solo-qeueing players. This occurs because there are less players as you advance ranks, and because players at higher ranks are more likely to have premade squads. Thus, if you solo queue as a Plat player, you are more likely to get a Gold teammate than a Diamond teammate. This obviously makes it harder to progress simply based on the queuing system, as you can still go up against premade squads of diamond and plat players.
Moreover, the tiers are essentially meaningless. Theoretically, if you move from Plat IV to Plat III, you should be able to move to Diamond IV with the same performance as neither the RP nor the matchmaking changes between tiers.
The apparantly fix to this would be to make tiers affect matchmaking, such as queuing within +/- 2 tiers. Thus, if you are a Plat IV player, you can queue with high Gold players and fellow low Plat players. Once you are Plat I, you can queue with Plat players as well as low Diamond players. This makes tiers matter, as they will progressively get harder. Importantly, it also helps your solo-qeueing as you are less likely to be stuck with teammates significantly below your rank.
A solo-qeueing Plat I player who just had 3 games in a row with Gold teammates.