Yes this is possible using either a base controller class that all your controllers inherit or by creating a custom attribute that you decorate your controller with.
Base controller:
public class BaseController : Controller
{
   protected override void Initialize(System.Web.Routing.RequestContext requestContext)
   {
       // verify logic here
   }
}
Your controllers:
public class AccountController : BaseController
{
      // the Initialize() function will get called for every request
      // thus running the verify logic
}
Custom Authorization Attribute:
public class AuthorizeAccountNumberAttribute : AuthorizationAttribute
{
    protected override AuthorizationResult IsAuthorized(System.Security.Principal.IPrincipal principal, AuthorizationContext authorizationContext)
    {
           // verify logic here
    }
}
On your controller(s):
[AuthorizeAccountNumber]
public class AccountController : Controller
{
      // the IsAuthorized() function in the AuthorizeAccountNumber will 
      // get called for every request and thus the verify logic
}
You can combine both approaches to have another custom base controller class which is decorated with the [AuthorizeAccountNumber] which your controllers that require verification inherit from.