You can create a second set of mail credentials in you .env file
MAIL2_HOST=some_host
MAIL2_PORT=some_port
MAIL2_USERNAME=some_user
MAIL2_PASSWORD=some_password
MAIL2_ENCRYPTION=tls
Then according to the SwiftMailerDocs, in your application create a new Swift_SmtpTransport instance
$swiftTransport = Swift_SmtpTransport::newInstance(env('MAIL2_HOST'), env('MAIL2_PORT'), env('MAIL2_ENCRYPTION'))
->setUsername(env('MAIL2_USERNAME' ))
->setPassword(env('MAIL2_PASSWORD' ));
The create a new Swift_Mailer instance
$swiftMailer = new Swift_Mailer($swiftTransport);
Then use the swift mailer setter in Laravel Mailer to assign the new swiftMailer instance. Laravel Mailer API
Mail::setSwiftMailer($swiftMailer);
At that point you should be able to use the Mail facade as you usually would to send with this new account.
Note: I didn't test this but it should work.