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I want to ask a question about Apache Load balancers with stickysession cookie

Dear all,

I want to ask a question about Apache Load Balancers with stickysession
cookie.

Is it possible to connect to 2 different sites (both sites are served by
Apache Load Balancers with different stickysession cookie) from the same
browser window ?

In order to be more precise.

I can connect from a browser window (tab) to ONE site that is served by an
Apache Load Balancer with a stickysession cookie. Can I Press (for instance)
a button on this site in order to also connect to ANOTHER site that is also
served by an Apache Load Balancer with a different stickysession cookie ?

I have searched everywhere but I cannot find any clue.

Thanks