Answering your question - yes, it's possible. There are at least two ways of doing it more properly.
If you would like to perform a "hard" routine on checking fields in the PHP code, there are also two ways of doing that:
- Modify bb_func_checkusr.php and apply some custom modifications adding new fields and values to provide new custom errors (you must know a bit of miniBB working principle to do it properly) - this will exclude this script from the easy updates though;
- Modify bb_plugins_user.php and add some new codes to handle all related fields and values at the non-destructive level - this will allow to keep easy upgrades in the future.
Since your task is customized and I don't have an idea what kind of fields you have on form, I can't recommend more. Also, if you need exact codes, you may refer to our private/paid customers support for that.