When you ask for a super-type of two items, be they people, concepts or something else, you imply the existence of a taxonomy that includes both as well as an item that is an ancestor to both.
We can therefore recast the question as "What is an appropriate taxonomy for people and businesses?"
First, what is a taxonomy?
Taxonomy (from Greek taxis meaning arrangement or division and nomos meaning law) is the science of classification according to a pre-determined system, with the resulting catalog used to provide a conceptual framework for discussion, analysis, or information retrieval.
- Margaret Rouse
There isn't really a widely-used taxonomy that includes both people and businesses, so it's natural to ask how one might set up such a taxonomy.
Two of the predominant types of relationships in knowledge-representation systems are predication and the universally quantified conditional. Predication relationships express the notion that an individual entity is an example of a certain type (for example, John is a bachelor), while universally quantified conditionals express the notion that a type is a subtype of another type (for example, A dog is a mammal, which means the same as All dogs are mammals).
- Brachman, quoted by Wikipedia
(Although you use the term super-type, I take it that you would be happy for either style to produce a common word.)
We're now looking for commonalities, be it something that both are examples of, or a conceptual union of the concepts people and businesses. The problem is that the concepts are arguably more different than chalk and cheese - one is real and the other is a legal fiction. You need to go a long way up the taxonomic tree to get to a common ancestor, at which point entity starts looking reasonable. Your objection that it is "too broad" simply reflects the distance between people and businesses in any generic taxonomy. That is, they are ontologically rather distinct.
Taking one more step into this rabbit warren, let's consider the kind of ontology we can construct for your question. There are two basic types:
- domain ontology, which has a restricted universe of discussion (the domain); and
- upper ontology, which "describes very general concepts that are the same across all knowledge domains" - Wikipedia
A domain ontology, say restricted to taxation, gives rise to 'super-types' such as taxpayer, and it seems to me that an upper ontology gives rise to 'super-types' such as entity.
So the 'simple' answer to your question is that there are super-types for people and businesses. A deeper answer would likely need to delve into the fundamental nature of people and businesses. I've started to look at that, but further exploration of this topic is perhaps best left for another question, given the length of this answer as it stands.