There should be 3 to 4 Emperors.
Facts:
1. From
http://www.agbank.mn/agbankger/index.shtml Ogedei (3rd son) is born in 1187 (Beginning of LOCH).
2. Tuolei (4th son) is about the same age as GuoJing.
3. MongKe died in 1258 (end of ROCH).
4. From
http://www.yutopian.com/history/nansong.html, 4 Song Emperors reigned between 1163 and 1265. The first of the 4 emperors died in 1190, 3 years after Ogedei is born.
The uncertainty here is the age difference between GuoJing and Tuolei, and between Tuolei and Ogedei.