Can two of us work on one profile?
On a team, yes. Share the profile with a colleague and they can work in it, not just read it: they can run assessments, write goals and add notes. Deleting the profile stays with whoever owns it.
Share it the usual way: open the profile, choose the three-dot menu, then Share with team. Who on my team can see my profiles? has the steps and how to take a share back.
What they can do
The same things you can: open the results, start an assessment, create and edit goals, read the strategies, add notes and download materials. The profile turns up on their Profiles list under Shared with Me.
Deleting the profile is the one thing that stays with the owner. Team admins can also delete any profile in the team.
Sharing needs a team plan. On a personal plan there is nobody to share with, but you can still share a finished assessment report with anyone by link or email.