First edos to have an N number of thirds (range is 15/13 to 13/10, closest JI interpretation that is consistent in the edo’s odd limit is chosen):

Number of thirds Edo Thirds
0 0 or 1 None
1 3 5/4
2 5 7/6, 9/7
3 15 7/6, 6/5, 5/4
4 19 7/6, 6/5, 5/4, 9/7
5 26 7/6, 6/5, 16/13, 14/11, 13/10
6 29 15/13, 13/11, 6/5, 16/13, 14/11, 13/10
7 (41) (~)
8 (41) (~)
9 41 15/13, 7/6, 13/11, 6/5, 11/9, 5/4, 14/11, 9/7, 13/10

This list could be used to get the minimal edos to add more flavours (of thirds).