How do you put a new drain into a concrete basement floor?
Yes, you must cut through the concrete floor and excavate a new drain line to connect to the others. The drain for the existing sink and toilet should be adequately sized. You will need to tie the new shower drain in before the connection for the toilet (can run a toilet drain past a sink or bath drain). The area under the drain hub for your shower will have the p-trap installed, and you will have to maintain proper slope for the new line, so you may need to raise your shower floor to make it all work if they did not plan on it originally.