You can do this if you have an alternate account. Then you load the game from your main account, then join the table with the other account, and so play both sides. You need one account to have access to all the cards of the game though. The other account can then be a free one, so is made in 5 minutes.
You need to use two different browsers for that, as otherwise the browser may get confused (at least it used to be that way, I haven't tried it in a long time).