Mass text App/Program

Hi-

I run a business which requires me to send multiple mass texts out to my clients and I am looking for a better system. I'm curious if there is a way or some kind of app that would allow me to send out mass texts without the recipients:

a.) being able to see that they are in a mass text/see the other clients phone numbers

b.) would allow me to pull/remove replied clients from the group text onto their own text without disrupting the rest of the group within the text

c.) can be distributed/run through my phone (ie would allow replaying clients to see and respond to a number provided via the texting service)

Used Callfire once and have heard of a few things but wanting some more insight as to what would work best for my company.

Thanks