Sure you can; you'll need a powered USB hub though, to power up all these adapters, and you'll have a hard time achieving 100mbit throughput. USB 2.0 is 480 Mbit/s half-duplex, over one cable between RPi and the hub, no matter what communicates with what, e.g. transmission between two local ports.
Enumerating and addressing all these devices in Linux before setting up routing will be a drudgery too. Doable, but IMHO not worth the effort.
Personally, I believe you'd be far better off using one USB-Ethernet adapter, turning RPi into a router with 1 WAN and 1 LAN port, and one dumb network switch for creating the remaining 4 LAN ports. That way you get 100mbit throughput to WAN and save up on 3 USB adapters.
Still, this all is an interesting but not very useful exercise. Getting a dedicated router where you can replace the firmware with your own will be more fault-proof, easier, and cheaper.
(4 WAN and 1 LAN)
A standard switch will also work with VLANS or simple IP masking but I think the OP has no idea about networking. I suggest to use a router like MicroTik or pfSense for this with Gigabit ports and software that knows how to handle load balancing.