I am not an expert in how WPA works however I don't think there is a way to set up an AP which accepts any password; the 4-way handshake is a lot more complicated than just client sending password to AP and asking if it's correct.
Traditional evil twins work by already knowing the password and are used for launching different kinds of attacks on clients, not finding out the password for an existing network.
There are tools designed to make this process of luring a target onto a network the attacker controls easier. Notably Airbase-ng and Wifish. Wifish in particular exploits the way wifi clients try to reconnect to previously known networks. As I recall it works well for unsecured and WEP protocols. The webpage makes vagues mentions to WPA too but I don't remember the details, I saw the presentation a while ago.
This is something you can investigate if you are interested. You can find the presentation on youtube.