Is there something in between external and shared storage?

Is there something in between external and shared storage?

On a computer setup I'm aiming to achieve 2 things:
I want high speed external storage for my main PC. USB 3.0 fits well.
Also be able to share that storage with other devices. LAN speeds would be
fine.
I've come up with several approaches like:
PC as 24/7 server: Fulfills both, could even work with an internal HDD,
but It's not energy efficient.
Network drive & Router: Fulfills second, but can only output at Gigabit
Ethernet speeds to my main PC.
Regular USB 3.0 HDD & USB 3.0 capable router: Seemingly, fulfills second,
but can only output at Gigabit Ethernet speeds to my main PC.
Do you have any other idea?
I don't understand why routers do not output anything above Gigabit ethernet.