Deploy an application on a machine for each client

I have a question. I have an application in rails that will be used by several different clients. I'm studying the best environment to put the application in the air. Does Heroku have the possibility of deploying the same application on a machine for each client? The only way I thought was to clone the project in different directories on the local machine and start the heroku with the client domain in question but this way there would be a lot of redundancy of the same code. If anyone can give me strength, I appreciate it.