Yes, Sleeper supports Taxi Squads.
Taxi squads, also known as practice squads, are becoming more popular in dynasty fantasy football leagues and offers the option of stashing rookies in additional slots that don't count against your roster limit.
There are 3 settings that affect Taxi Squads in League Settings.
1. Taxi Slots
You can turn on Taxi Squads by setting the number of Taxi Slots.
2. Taxi Deadline
This is the deadline for which you must finalize your Taxi Squads for your rookies.
The default is Week 1 of the season, but this can be adjusted to a different week.
3. Taxi Years
This is the number of years you can stash a player until they are forced to come off the Taxi Squad. For example, if Taxi Years is set to 3 years, then a Rookie must come off the Taxi Squad in his 4th year or the owner cannot make lineup changes or add/waiver players.
Note: At the moment, you cannot add direct-to-taxi. However, what you can do is increase the bench by one, add rookies, and move them to taxi one by one.
Additionally, another way is to do a separate rookie-only draft, this would allow your team to go over the limit since it's from a draft, giving you the ability to move rookies to taxi.