Storing Dynamic data in relational database (SQL Server 2014)
It sounds like you are looking for an Entity-Attribute-Value (EAV) data model design.  Aaron Bertrand has a great post on this which I suggest you look through and see if a similar approach will fit your needs.

As a DBA, I have a deep-seeded hatred for this approach, but sometimes it makes the most sense for the situation at hand.

If you can convince whoever controls the budget to upgrade to SQL Server 2016, there are some new features that take advantage of JSON data, which can give you even more flexibility.