Since I cannot leave a comment, I will use the Answer form.
I had a similar task and looked at several multi-port ICs to build onto a board, I ended up using a USB hub and multiple USB to serial (RX & TX) adapters which works fine. I use 8 to 24 of them on several products I support on a Raspberry Pi. At the slow rate of 9600, the Pi will not have issues.... I don't.
One thing you may find useful is to be able to "fix" which USB is connected to which serial port. Otherwise the ports "move around" after each boot due to the way the USB interface initializes.
Use this link for a good start on how to keep the ports from changing.
It is also important to be VERY careful when selecting the USB to Serial converters because the Pi will not work with many of the "cheap" versions.
I used my o'scope and found that the RS232 chips in them are VERY poor, only allowing a couple of bytes to pass before the voltage they output slowly declines until the receiving device can no longer read the data.
These same "poor" USB to serial converters will work on my laptop or my desktop, but not on the Pi. Something to be aware of and watch for.... It was difficult to find this problem because the converters work on my laptop or desktop, but not on the Pi, BUT the "better" converters work on the Pi perfectly...
I use powered USB hubs in my products, and the Pi will not work with the cheap converters plugged into the hubs either... which is strange! To me it makes no sense what-so-ever, but this is the experience I have had.