I just wrote a suggestion to Beeminder authors to add group goals. Two options:

Competitive mode: All people make the same commitment. The only difference between individual commitments is that all lines are displayed on the same graph. (So in addition to avoid losing, you have a motivation to get more points than your friends.) If a person loses, others continue. If only one winner remains, they get an option to cancel the commitment after one week (because the motivation of competition is gone; and maybe the rest of the group wants to start the game again).

Cooperative mode: A commitment fulfilled by the group together; a sum of individual contributions must reach a given limit. The system does not care about who did what, they either win as a group, or lose as a group. However, the individual contributions are displayed, so they can translate to group status.

This could translate conscientiousness into a group status, thereby encourage conscientiousness. (Well, assuming that no one cheats when entering data, etc.)

The group goals could work also without the Beeminder system. Just make a graph where all group members can report their progress, without any time limits. In the cooperative mode, the game ends when the sum of contributions reaches a specified value. In competitive mode, when the first player reaches the specified value, others get an additional week to keep up or lose.

(In a competitive mode, players could specify handicaps, for example that one point by person A is equal to two points by person B. Maybe it would make some sense in a cooperative mode, too.)