[AttributeUsage(AttributeTargets.Method | AttributeTargets.Class, Inherited = true, AllowMultiple = true)]
public class MeuAuthorize : AuthorizeAttribute
{
    private String[] _permissoes;
    private MeuProjetoContext contexto = new MeuProjetoContext();

    public CustomAuthorizeAttribute(params String[] permissoes)
    {
        _permissoes = permissoes;
    }

    protected override bool AuthorizeCore(HttpContextBase httpContext)
    {
        var baseReturn = base.AuthorizeCore(httpContext);

        var permissoesReturn = false;
        var permissoesUsuario = contexto.Permissoes.Where(p => p.Usuario.Nome == httpContext.User.Identity.Name).Select(p => NomePermissao).ToList();
        permissoesReturn = permissoesUsuario.Intersect(_permissoes.OfType<String>().ToList()).Any();

        return permissionsReturn || baseReturn;
    }
}

[MeuAuthorize("Usuário", "Gerente", "Administrador")]
public ActionResult MinhaAction() { ... }

[MeuAuthorize]
public ActionResult MinhaAction() { ... }