Yes, but most of them are data-use apps that dont use the free texting service that the stock app and Verizon Messages uses. I refer to Textra, Handcent, etc....
Handcent (now called Next SMS) uses SMS. I know this because when I turn off Mobile data, messages still get sent and received (no WiFi here either).
I've been using it for years now and think it's the best texting program out there. Adding custom tones to individual users is easy, too.
NextSMS...good to know.
I don't know if it is still an option, but the Samsung phones could at one time assign individual text messages tones to the individual contacts through the People/Contacts application.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.