Thanks Sander for your valuable comments, suggestions and the reference to your blog. I will definitely consider another design, probably using DB Partitioning.
I think I've got now the correct answer to my question: SPO's characteristics are not shown in the "Identify" screen because there are too much SPO's partitions. When the partition number becomes greater than the multiprovider's part providers limit (what that number exactly I haven't found yet), then the screen won't let you assign the SPO characteristics.