Achieve single node field edit to have different values for each user?
As you described it, it is not possible with core Drupal's field system. While you can create a node editable by many users with a multivalue field, the field (and its values) do not have property of ownership. Thus, your requirement to see different values for different users would not work.

There are alternative ways to achieve this. One path is to add 2 fields to the user profile.


Activity: an entity reference to your activity node.
Value: the user's field value you want to capture.


If the values are inherent single property of a user, you can add them directly to the user profile and use a Field Group to present it as combination of fields for the user to enter.

If the user can have many different Activity &amp; Value combinations, you could use either use something like Field Collection or ECK/Inline Entity Form to present an embedded form in the user profile where users can add many different Activity/Value combinations.