If contacts are saving to SIM, then it's not possible to have more than one number per contact. It's not a problem of the phone but that's a limitation of saving to SIM cards. Doesn't matter what phone you use, SIM cards only support one data line per contact. You also can't add contact pictures because SIM cards do not have enough storage for pictures.
Also I would advise against saving to SIM because not only do SIM cards fail and make things irrecoverable, smartphones are moving to sim-less phones using e-sim. So no more sim cards in a few years.
To have multiple numbers per contact it should be saving either to device or Google. Google is better for you because I think Samsung cloud started on thr S6 so device contacts on the Note 4 is likely not auto-backed up to Samsung servers. Then press edit and then the plus sign beside the entry field for the number.