Full Idea
Since properties themselves can have properties there is a well-known division in the theory of properties between those who take a typed and those who take a type-free approach.
Clarification
'Typed' means some properties would be 'higher-order'
Gist of Idea
Since properties can have properties, some theorists rank them in 'types'
Source
Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 08.5)
Book Reference
Hofweber,Thomas: 'Ontology and the Ambitions of Metaphysics' [OUP 2018], p.226
A Reaction
I take this idea to be about linguistic predicates, and about semantics which draws on model theory. To see it as about actual 'properties' in the physical world makes no sense.