If primary and secondary root switches with priority 16384 both experience catastrophic losses, which tertiary switch can take over?

A switch with priority 20480 is a valid STP priority value. In a scenario where switches with lower priorities than 20480 (including the primary and secondary 16384 switches and any other intermediate lower priority switches) have all failed or are unavailable, the switch with priority 20480 would then become the lowest available priority and could take over as the root bridge, thus acting as a later-stage 'tertiary' backup.

A switch with priority 8192 would be preferred over 16384 and 20480, making it a primary or secondary candidate if lower priority options are absent, not a tertiary one after 16384 fails if other lower ones exist.

A switch with priority 4096 would be the most preferred root among all given options, taking over as the primary root, not a tertiary one.

A switch with priority 12288 would be preferred over 16384 and 20480, making it a strong candidate for a new primary or secondary root, or the direct next-in-line backup, not the 'tertiary' if lower options are available.