Multiplayer just gives you more people who could work together or against each other.
Research itself would be based on either your own Stats, or on the Stats of whatever NPC Town you’re in (since those can do Research too, though I will make them mostly stagnating).
There will be some Mechanic and all I can say is that I will try to balance it for single and multiplayer equally.
Thing is, if someone else Researches ahead of you, you can just go there and try to steal their Science Documents, or the Machines to reverse Engineer them. This would be the main way of catching up.
If the Player that is ahead also has an NPC Town, it will be significantly easier to sneak in and just steal the Science Stuff or Machines, especially since those players usually tell their NPCs how to do the new Tech Stuffs, since the NPCs cant work with what they dont know, meaning the NPCs will have Books containing Info about whatever Tech they are producing.
And since stealing is kindof intended, there will be effective measures for NPCs to defend themselves. Not to mention you cant just grief a House to get inside, that’s way too minecrafty.