Part 1:

If there exists a rule entitled “Social Structure”, then add a subrule to it with the following text:

Grudges.
There is a GNDT column called “Grudge” whose legal values are the names of all non-Host Contestants.  A Contestant is said to have a Grudge against any one or more Contestants named in eir Grudge column.  A Contestant may not simultaneously have a Grudge against, and Support, a particular other Contestant: if any change in Gamestate required or permitted by the Ruleset would, but for this sentence, cause a Contestant to simultaneously have a Grudge against, and Support, a particular other Contestant, then the Grudge will exist and the Support will revert to its default value).

Part 2:

Change the sentence in the rule “Social Structure” that presently reads:

A Contestant’s Support defaults to the Contestant immediately below them in the GNDT, skipping the Host, with the bottom Contestant defaulting to the top Contestant.

so that it reads:

A Contestant’s Support defaults to the Contestant immediately below them in the GNDT, skipping the Host and any Contestant whom the Contestant has a Grudge against, with the bottom Contestant defaulting to the top Contestant.

Deliberately omitting the mechanics of how one can acquire or lose a Grudge.  This can be fleshed out later.