web page relay to multiple client

This is coming from someone not very familiar with cookies or session handling in web,but I was wondering if it's possible to, say, login using computer A to a website which doesn't allow one account logged in from two places simultaneously, then A forward the logged on page to say 10 client which can be anywhere on the internet, and those 10 client can interact with the website as if they logged in normally. (A could be seen as an account login proxy if you will)

If this is possible, what is the least expensive(straight forward) way of implementation? (obviously other than remote desktop)? Would A sharing cookie with clients be enough? and what is the most robust way? preferably the clients only need browser.

If this is not possible, why is that the case? Is it because of the cookie? Or Javascript?

//All scenario assume the website is serious like facebook or amazon, so behind it there is some major database operation going on, meaning state consistency would have to be considered.

What prompt the question for me is that I can use two different browser on same computer to log into a website that doesn't allow two place login, and in each one of them I can operate as usual, even the change made in one browser can be seen in another immediately after refresh or page loading. So I can't think of a reason why these two browser can't be in two computers. But I can't come up with a way to implement this.