You could use a RAID enclosure like
OWC that connects via USB to a router. Many routers offer Time Machine support (but not all). Using a RAID enclosure enables you to put a 2 or 4 (or more) disk array on your network, with added speed in the case of a 4 disk array using RAID5.
Obviously, Time Capsule and AP Extreme allow you to share USB connected drives for backups, in addition to the built in drives on Time Capsule. Like above, a RAID enclosure attached via USB will do the trick.
Synology has some pretty slick routers that not only support Time Machine for USB connected drives, but can also share over the internet, similar to Apple routers. As Synology is a NAS manufacturer, their routers offer many of the NAS functions on top of a very good wireless router. Synology routers offer USB3 ports (Airport is USB2).
Synology and QNAP offer an array of dedicated NAS that support Time Machine, and can connect to your LAN via Ethernet. Once connected, you can access them from any device that is either connected via Ethernet or WiFi to your LAN. There are other NAS out there, but these two are probably the most preferred NAS providers out there. Some NAS are powerful enough to run Virtual Machines if you need that sort of thing.
I have used a QNAP NAS for a few years, and am considering a Synology RT2600AC router to replace my Time Capsule and QNAP.