Решил проблему так:
Контролер авторизации
class SocialController extends Controller
{
    public function index(SocialService $socialService, $client, $provider)
    {
        $socialService->setConfig($client, $provider);
        return Socialite::driver($provider)->redirect();
    }
    public function callback(SocialService $socialService, $client, $provider)
    {
        $socialService->setConfig($client, $provider);
        $user = Socialite::driver($provider)->user();
        if ($u = $socialService->saveSocialData($client, $user)) {
            Auth::guard($client)->login($u);
            return redirect()->route('profile.index');
        }
        return back();
    }
}
Сервисный слой:
use Illuminate\Support\Facades\Config;
use Illuminate\Support\Facades\Hash;
class SocialService
{
    public function saveSocialData($client, $user)
    {
        if ($client == 'student') {
            $model = new Student();
        }
        if ($client == 'teacher') {
            $model = new Teacher();
        }
        $email = $user->getEmail();
        $u = $model->where('email', $email)->first();
        if ($u == null) {
            $data = [
                'first_name' => 'First',
                'middle_name' => 'Middle',
                'last_name' => 'Last',
                'birth' => today(),
                'email' => $email,
                'password' => Hash::make('secret123'),
            ];
            return $model->create($data);
        }
        return $u;
    }
    public function setConfig($client, $provider)
    {
        if ($provider == 'vkontakte') {
            $clientId = env('VKONTAKTE_CLIENT_ID');
            $clientSecret = env('VKONTAKTE_CLIENT_SECRET');
            $redirectUrl = 'http://127.0.0.1:8000/auth/'.$client.'/vkontakte/callback';
        }
        if ($provider == 'google') {
            $clientId = env('GOOGLE_CLIENT_ID');
            $clientSecret = env('GOOGLE_CLIENT_SECRET');
            $redirectUrl = 'http://127.0.0.1:8000/auth/'.$client.'/google/callback';
        }
        Config::set(['services.'.$provider => [
            'client_id' => $clientId,
            'client_secret' => $clientSecret,
            'redirect' => $redirectUrl
        ]]);
    }
}