Is it possible to have more than one composite primary key

I have a table with about 30 columns of data. I did not design the table, as it is a legacy system.
This table already has a primary key which is a composite key of four columns of data.

So here are some questions. Is it possible to have another Composite key in the table? You see, I have two other columns of data, and
it would be nice if these two other columns of data were designated as a composite key. Basically the columns are related to property rentals,
and for each property their is associated a unique email address. So each property id might represent an apartement complex.
And I just need to ensure that for each property id, the same email address is not used more than once.In other words no one living in an apartement
complex can share the same email address

These are the columns I would like as a composite primary key.
Column Name : PropertyId
Column Name : EmailAddress

Something to keep in mind is that I have a situation where many of the EmailAddress columns currently contain null data. Which I am sure
would not be acceptable for a composite primary key.

Can an expert or two give me some feedback on my question. As I don't know how to approach this.