I'm not an expert, however I've gone over the application guide and found no mention or restriction to applying to multiple streams. SINP simply does not mention it. The only thing close to this is Question 21 under General Questions (http://www.economy.gov.sk.ca/immigration/sinp-general-questions) which talks about applying to SINP while under processing for another Federal programs. Aside from that I found nothing that states you can't apply to multiple streams.
OASIS currently does not allow you to have multiple applications under the same account, even though it says "Summary of Applications". So if you do decide to apply you'll have to create a different OASIS account.
For the record, I created a new and separate account on OASIS and have already applied while still awaiting an answer on my EE application.
Do they ask for having express entry profile?
What you said?
Note: I answered yes to applying previously to Provincial program, and picked SINP from drop-down menu. Then entered the date of application, my name, application status (Application Received), and reason for status (no update thus far).
Hope that helps!