How to Fish officially supports up to 8-player lobbies as of Patch 1.0.4. Steam lists Single-player and Online Co-op, and Patch 1.0.5 adds invite-only private lobbies.
Max players
The confirmed maximum is up to 8 players in one lobby. This is lobby capacity, not the current number of players online across Steam. Use the live player-count page for the separate concurrent-player measurement.
Patch 1.0.4 added the 8-player support. If an older answer says four players or suggests a mod just to reach eight, it predates that official update.
Do you need a more-players mod?
No unofficial mod is needed for the officially supported capacity of up to 8 players. This site does not distribute lobby mods, installers, patches or modified game files.
A mod that promises more than the official limit is a different, unsupported task. It may affect compatibility, saves, networking or other players, so it is outside this guide's verified route.
Solo and online co-op
Steam lists both Single-player and Online Co-op. You can follow the same island, bait, boss, achievement and money guides alone or with a group, but the pacing and pressure can differ with more players.
For a solo boss task, open the focused Piranha boss guide or Pufferfish guide rather than treating lobby capacity as a fight strategy.
Private lobby boundary
Official Patch 1.0.5 added a private-lobby setting. A private lobby is invite-only, so joining that session requires an invite. This is a capability note, not a complete lobby administration guide.
Change the session type deliberately
Patch 1.0.5 also added session-type settings in the game's server settings. Changing the session type requires a restart. Make that change before the group settles into the next task.
If joining a lobby produces a black screen, use the join-screen checklist for the official patch and Steam-relay checks.
Quick questions
What is the How to Fish max-player count?
Up to 8 players per lobby, according to official Patch 1.0.4.
Can I play alone?
Yes. Steam lists Single-player as a supported mode.
Can I use a private lobby?
Yes. Patch 1.0.5 added invite-only private lobbies.
Does changing the session type need a restart?
Yes. The official session-type setting requires a restart after it is changed.
Is max players the same as player count?
No. Max players is the capacity of one lobby. Player count is the number of concurrent Steam players across the game.