Another convoluted approach would be to establish a linked server definition back to itself (the same server).
Then you can do an OPENQUERY to run your sp.
The mainline query will them treat the sp results as a temp table, to which you can JOIN, as necessary.
However, I wouldn't do this with large sp's producing large resultsets,
as it is very inefficient. I have also successfully used OPENQUERY to JOIN to DBCC output, such as DBCC INPUTBUFFER.