Three possible meanings for what you are asking that I can think of:
- "I'm going to swap the SIM back and forth and take the phone that suits my mood the best today" --- carrier-dependent. AT&T allows this, as would most carriers, I suppose, but I think they limit the number of times you can swap SIMs back and forth, and of course you want the SIM to be the same size (not sure on that). Check with your carrier on whether they care how often you move your SIM from phone to phone.
- "I want both phones to ring simultaneously and be assigned the same phone number" -- there are workarounds for this like using Google Voice and forwarding it to two independent phone lines, one for each phone, but no carrier I know of will send the same call to two independent IMEIs. You'll need two lines, or see the next option.
- "I want to use data on both devices at the same time and receive carrier calls on one". -- Easy. Get a tethering plan on the device you want to receive calls on, and tether the second one to it and it doesn't need a SIM at all. You can even make/receive Google Hangouts Dialer calls on the tethered one.