Router with 2 (or more) interfaces in same network

["Sugar, Sylvia" <truesylvia () yahoo co uk>]

Hi,

I am curious to know if its possible to have a router with its two interfaces, say configured as, 
1.1.1.1/16 and 1.1.1.2/16. Theoretically, i see nothing which can stop a router from doing this.
But practically, is it of any use? And if used, then, when and why will somebody want to use such
a kind of configuration?

Would appreciate if somebody could enlighten me on this.

Regards,
Rasputin

P.S.
I have a customer who insists he wants to do this, without providing any explanations!

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