jeannieniles I've done exactly what you want to do. You are right, the points only give a standard room. Sometimes you can book that online, and upgrade one tier (such as to concierge level) for a given extra cost per night, but it doesn't cover suites. However, what I have done is contact the hotel before booking and tell them what I want to do. They have quoted me a price for upgrading to a suite, then I have booked with points online and told the hotel the confirmation number. The hotel can then get into the booking, amend the room type, and add the additional cost per night. It has always worked for me here in the UK.
Also, and I don't know if this is suitable or not, there is the new "Points and Cash" starting soon. Until it starts I don't know how it works with booking anything other than a standard room.
Hope that helps.