It is entirely possible that more countries will leave the European Union. Now that it has been weakened by the UK's exit, more exits are likely to follow. If the EU begins to weaken and crumble significantly there could be a mass exit by many of the countries that a currently in the EU.
I think that if things go well with Britain leaving the EU, other countries will follow, especially countries that consider themselves harmed by being part of it. Many countries do not like the way the union has worked out for them, and feel like other countries are taking advantage of them. If they see a way to leave without undue harm, I think that's what will happen.
The problem with the EU is that the backbone of the union (namely Germany) is tired of carrying all the weaker members that don't want to produce as much. This leads to resentment and the Germans demanding by law to get better treatment, which defeats the whole purpose of the union to begin with. The EU should break up but retain the movement laws and simply support competition and free movement.
Following a trend set by Britain's exiting the European Union, as well as the Election of Donald Trump as America's next president, it seems that Western Europe is as well becoming more align with right-wing policies. As such, the EU will likely become destabilized, as more conservative rulers in European countries seek an exit.