How many people can I invite to edit my chart?

It depends on your plan. The free plan allows no collaborators, the Planner plan allows three, and PlanSeats Pro has no limit. View-only links are not collaborators, so share as many of those as you like on any plan.

On the free plan, share a view-only link with your partner for now; upgrading to Planner at $8.99 a month opens the three invitations.