Games with Mixed Couch/Online Coop Mode

Helldivers.

Recently got bro-force and It works if you can manage to get sorted out.

Use http://www.co-optimus.com/system/4/pc.html.
Go to "add filter" and pick "Combo Co-Op". You'll get a list with all games that support simultaneous off- and online co-op.

Games Tested and seemed not to work this way:

Monaco
BattleBlock Theater (Only Competitive)

Well, Battleblock only has two player co-op, so that's not surprising. :P
Castle Crashers is the only game from The Behemoth which offers co-op support for more than two players- both Pit People and Battleblock only offer PvP support for players past that.

Golwar's already gave the suggestion I was going to, but I'm going to add "remember to check the filter to active after you add it". ^.^
Unfortunately, the list co-optimus offers does seem to be somewhat incomplete, though. :/

The first Dungeon Defenders, don't know about the second one.

Factorio and anno 1404 (dawn of discovery venice), these 2 games is definitely the way to go if you have a alot of time to play. requires you and your friend to work together constantly to get things done.

Victor Vran ARPG - played it on controllers

Nearly any Local Co-op game can be played over net using Nvidia Share Play, tested and confirmed with Nuclear Throne.
It´s an experimental NVIDIA feature that only works on fullscreen games (not borderless windowed) and the receipient needs to use chrome browser, but other than that, it was awesome (when it worked that one time!) :D

Thanks for all the responses! I will check some of these games and links and update the table by time.

Push
We're running low again on this type of games. Any new suggestions? (Updated the main table)

You said you're looking for PC games but if you play on consoles, Borderlands is a solid option (I personally recommend BL2). Technically you "can" get it to do local multiplayer on PC, but it's a hassle. Tried to set it up like that for a friend and tldr; you adjust the launch settings to run two instances of the game simultaneously. (in hindsight, it might actually work as long as you have 2 screens to play on?)

Move or Die and StickFight: The Game are very fun party games that you can play local/online.
I know Move or Die you can play local multiplayer and then online at the same time.

Is this list still being updated?

Duck Game fits this bill quite well and is incredibly fun. I think whoever has the local player needs to host but I’m not 100% sure.

Grim Dawn
some of the civilization games
Age of Conquests IV has online but the manual talks about 2-player online games
Ticket to Ride?

Brawlhalla, you can coop with somebody in the same device and fight against people who are away using the Internet. It's free nowadays.