The response they give me and pretty much everyone else is they want one MEID/ESN number associated with one phone line for security and fraud reasons.   At one point I asked to have an extension phone "one number shared by two phones" similar to what you would have on a landline.    They gave me the exact same response.   They want ONE phone identified with ONE MEID/ESN at a time.   You can read their verbiage about this online as well.  Here it is below.   This is for the Extension phone question but it is the same response they'll give you for two lines on one device as well:

Does Verizon Wireless offer extension phones?

We have thoroughly weighed the costs against the benefits of offering this feature. We have made the decision not to offer the capability to use two wireless phones with one wireless phone number. The current wireless system we use identifies the wireless phone's Mobile Equipment Identifier (MEID) and matches the MEID with the wireless phone number. This process is integral to our system as it helps protect against wireless phone misuse and fraud.