Hey Netfox,
Level streaming does function in multiplayer games. However, when any player steps into a level streaming volume, connected level will load for every player, even though other players are not inside that volume. Logic for streaming volumes is hardcoded to replicate streaming state changes to all clients, so level streaming in a multiplayer game may not be useful without changing source code.
You can, however, achieve a similar effect with some creative use of Blueprints and Trigger Volumes.
This way streaming level will only be streamed on client when local character steps into Trigger Volume.
Hope that helps get you started!