To do it without buying another product, try this. When you’re doing House Creation with your players:
When they decide what type of house (Nascent, Minor, Major, etc), have them name another house (if they picked Nascent or Minor, name the House they’re vassals to; if Major or Great, name one of their vassal Minor Houses or a peer Major House) and give a one-sentence definition of their house’s relationship to the newly-named house.
When you assign domains, name another House (or Faction) that’s somehow related to their House’s Primary Domain(s), and define that relationship as above. Then do the same for any Secondary Domains. This new House/Faction should have some relation to the Domain - they might be a major customer, a rival, or a supplier of something your House needs to be able to function in that Domain.
When you describe your House’s homeworld, name an additional House or Faction, and this time define that House’s relationship to the players’ house.
When you describe your house’s Banner and Arns, have each player in turn define a relationship between any two Houses/Factions on the map.
When you describe your House’s traits, again have each player in turn define a relationship between any two Houses/Factions on the map.
When you define your House’s Roles, each player in turn names an NPC who fulfills the same role for one of the other Houses/Factions on the map, and defines a relationship between that person and someone else on the map.
Finally, when you define your House’s enemies, either select a House/Faction already on the map, or create a new one and define a relationship between the Enemy and your House, and also between the Enemy and one other House/Faction on the map.
That ought to provide enough material for a ton of intrigues!