What you should do is to have the foreign partner(s) not eligible for SSN apply for an ITIN.  Here's an excerpt from the instructions for K-1:

Foreign partners without a U.S. identifying number should be notified by the partnership of the necessity of obtaining a U.S. identifying number. Certain aliens who aren't eligible to obtain SSNs can apply for an ITIN on Form W-7, Application for IRS Individual Taxpayer Identification Number.