Cable Modem From Comcast - Unable To Add Additional Port?

Our small business just moved into a new building and I am in charge of setting up the network infrastructure. I am not new to computers or networking but I have never had to deal with this set up before.

Our current set up.We have a cable modem from comcast that has the Coax cable connected to it.The modem has 4 ports on it. The ports are connected to a built in 24 port switch that was already in the building. The switch has it's ports connected to outlets in the walls. Currently we have 4 computers on our network and since the cable modem had 4 ports it worked fine.

What we need? We will have another person join our office so I will need to activate one additional port on the switch that already exists. However, since all 4 ports on the modem are already taken, I have no way to add an additional port. They also want us to get wifi in the building.How I think I have to solve the problem (most likely wrong).I have to get another switch (like 8 port) and connect the cable modem to the switch using a cross over cable (if there is no designated internet port). Since I have the modem connected to the switch, I will have to move the 3 remaining connections to the switch.

Then I connect the 4 remaining ports on the switch to the existing 24-port switch that is already there. I will use one of the outlets in the building to connect an AP for Wi-Fi for better signal. Currently the modem and switches are hidden in a closet away from the office space and would mess up the signal.