Basecamp makes it very easy to add "companies" (other organizations) to a project, in additoini to your own company or organization.  And you can add as many users to each company for that project. And once you do that, you can then decide what level of access each of these additional company users should have. You can allow them to see and post messages, to-do's, and/or milestone events.

One different between what users in the account holder company (you!) and the additional clients or partners you add to a project concerns who the other users can assign to dos to. here is what the basecamp help page says:

 * Clients who have access to a project...

• Can edit/delete messages, to-dos, or milestones they've entered.
• Can check off to-dos or milestones that have been assigned to them by someone else. (So, if you create a to-do item, and assign that to-do item to someone on the client side, that person on the client side can complete that to-do item by checking it off.)
• Can assign to-do items or milestones to people inside their own company.
• Can not assign to-do items or milestones to people outside their own company.
• Can not change or remove something you've entered.

If this  restriction doesn't make sense, here is a workaround. Create a new user in the client company linked to the project lead from your company. Create a new user account in that client company, and put in the email address to the appropriate person in your company.  Give the name something like {your company abbreviation}(the other company abbreviation}admin. For example, dbdes_abc_admin. The users from the client company can then create assignments to the blanket admin person from your company. Your lead person will get the notifications and can then manage them from within his/her own original account.