Extend my personal renter's insurance to cover duplex tenants?

[Tim Johnson]

This may be a crazy off-base question but just want to get clarification.

I rent an apartment in Texas as my personal residence and cover it with a renter's insurance policy. I own a duplex in Oklahoma and I have a rental dwelling policy to cover that property. 

Talking with an insurance agent friend of mine, he mentioned that it is possible to extend your personal insurance coverage to cover other properties, even if it is a rental property. He said it's possible to save money this way while still covering both properties.

It seems crazy that I would be able to extend my renter's insurance policy to cover tenants. Especially if it's in another state.

Does this sound at all within the realm of possibility?