One way to do it is, if a player connects to the 'two player mode' so would he/she be able to see a list on players which he/she would be able to join.
One should be able to choose if they would like to be the Sandy man or Igor when joining. Now if two players want to say, play Igor then maybe their names should be displayed above the Igors or we could have it so that only one can be Igor and one can be the Sandy man.
When a player joins in it should say "<name> has arrived." Although I don't know if player one can play around until a second player arrives or if player one would have to wait until the second player joins.
Regarding items and scoring points to achieve higher rank in the pyramid so am I a bit unsure what will happen. Either nothing happens when the game ends or each player gets what they collected.
About the

I don't have any ideas on how the quest for this would go but if this suggestion ever would be implemented I could come up with ideas.

If there anything is unclear I will try my best to explain it better.