Router with 2 (or more) interfaces in same network

While it's a more common thing to do with hosts,
there are a number of reasons you might want a router with
multiple interfaces on the same network.

- Sometimes ugly things happen during reconfigurations,
e.g. replacing two routers with one bigger one.
Load balancing is more likely to want two interfaces with
the same IP address, but sometimes different addresses on the
same subnet makes more sense.

- Security monitoring / eavesdropping applications,
where one interface is listen-only or listen-mostly.
Usually promiscuous interfaces are enough to do this,
but there are remote monitoring applications where it might help.

- You may want different policies on the two interfaces,
and sometimes it's easier to do that with separate
IP addresses than differentiate by TCP ports or whatever
(e.g. VOIP on one interface, regular traffic on another,
with a LAN switch keeping them separate.) That's especially
believable if you're using an ISP that doesn't do
Type of Service bits, or multiple ISPs that don't peer with ToS.

- Ugly loopback thingies working around other limitations.
I've mostly seen this at Layer 2, with Cisco Virtual Trunking,
or building things in test labs.