Grind SotC: Fate-locked ways?

Fallen London
1

Hi, could I know what are the fate-locked ways to increase SotC?

2

A couple of the pets from Theological Husbandry will take you to SotC 10.

3

The Ocelot and the Owl will take you to 10. Other than that I can’t think of any useful SotC boosters that are fate-locked.