Could you use a cross-over cable direct from PC#1 to PC#2... maybe, but why? the ONLY reason I'd think to do this is i you don't have your own network (ex, on campus) and security or other settings on network are interfering (unlikely, but possible)... then .. maybe... with a bunch of caveats of it will take networking configuration outside the normal to get it to work (easy for someone who knows networking, not so much for others)
With typos, I'm no entirely sure the question
A typical modem usually only have one Ethernet port (and if multiple, it would be for link aggregation). Though the device maybe a modem, it would be more appropriate to call it a Gateway, if the device is BOTH a modem and an Ethernet switch for the LAN. In which case, unless known problem, I'd use the switch... then again... I don't trust ISPs. So I have a dedicated modem, and then my own personal router/firewall (business grade, not consumer), and then a separate switch behind that. And that is geeking out.. a bit.. granted :^) but even 25+ years ago with my first cable modem, I still had my own (consumer grade) router (with built-in Ethernet switch)... I recall doing cross-over cables back in the '90s... with more recent switches (this century), I've not had a reason/need