Groups and sharing accounts

My company uses groups to distinguish different client users.  So example, Client A is a group and Client B is a group.  I want each member in the separate groups to be able to share with other members in the same group, however I don't want either group to be able to see the other groups across my organization.  This is what happens...say I am a member of Client A, when I click on Sharing Status within my profile and click on the '+' button to add an email address, I then click on the down arrow next to the 3 horizontal lines.  Even though I am a member of group Client A, I can see the group for Client B and expand it to see the users in that group.  Anyway to avoid this and still allow users in each group to sign, edit and modify agreements within each group?