When we change the availability I guess it works like totally private or open to the world.
Can we have one more option in between like only available for the oDesk clients? Like it says on the popup screen “Do you want to make it public so clients can see you in search results?”
So that only the clients can see the profile in search results and other places.
If you go to your profile page, and click on the Edit Settings link...
and then look in the My Profile section, and click on the Edit link for that section...
You will see the "Public Access" option.
This is a dropdown menu which allows you to choose 3 options:
b) Only show my profile to oDesk users logged in
So... what you have asked for is already in place.
There already IS "one more option between".