differnet cookie - same VS

Hi,

 

I have one VS, and two services under this VS, and I'm using persistence cookie. for instance: aa.david.com will lead the user to pool - 172.16.1.1 bb.david.com will lead the user to pool - 172.16.2.1

 

for now the users getting the same cookie no matter they are entering (aa.david.com or bb.david.com)

 

Is there any option that they will get a different cookie for each service on this VS ?

 

Thank you.