That's doubtful. So let's take this proposition, that a group is a thing, and see if we can validate it's truth. We have "2", and we claim that it is a thing, a unity, one. ... — Metaphysician Undercover
We're talking past each other due to using different semantics. I'll be more precise. I'm basically presenting the physicalist ontology developed by D.M. Armstrong (see
this).
In Armstrong's ontology, everything that exists is a State of Affairs (which I've been referring to as a "thing"). A SOA has 3 types of constituents: a (thin) particular, properties, relations. None of the constituents exist independently of states of affairs. A SOA is a (thick) particular. ("thin" refers to the abstract consideration of that constituent of a SOA that is neither a relation nor a property; "thick" particular equates to a SOA, and "thick" is usually omitted).
Anything that exists is a state of affairs, and that includes the simplest objects (the "atomic states of affairs") and complex objects (higher order [molecular] states of affairs and conjunctions of states of affairs). If we treat the standard model of particle physics as describing the most fundamental objects of existence, then the atomic SOAs are those particles (the various quarks, leptons, etc). Even these fundamental ontic objects have properties (electric charge, color charge, spin, mass...).
A neutron is thus a second order SOA composed of those ASAs, while an atom is a third order SOA composed of neutrons, protons and electrons. The properties of the higher order SOAs are determined by the properties of their constituents (i.e. Armstrong is a reductionist).
A gaggle of 7 geese is a state of affairs as well - it has properties (such as mass, volume of air they displace,...).
Armstrong accounts for universals: they are multiply instantiated properties and relations. Multiple objects can have a -1 electric charge (e.g. each electron that exists), so "-1 electric charge" is a universal. Similarly, multiple states of affairs can have the property of being a conjunction of 7 lower order states of affairs. "7" is the property they have in common, and this is a universal.
Your statement, "We have "2", and we claim that it is a thing, a unity, one. In doing this, we deny the meaning of "2", that it refers to two distinct things, not one entity. " has no apparent meaning in this ontology. A state of affairs (a "thing") is not necessarily one thing - that would imply that only atomic states of affairs exist.
Either we describe the swans as individual objects, or we describe them as parts of a whole (an object, the family), but we cannot do both at the same time without contradiction.
I agree than an individual swan is not identical with the group to which it belongs. Each swan is a constituent of the state of affairs that is the group of swans. We can consider the mathematical relation that exists between one swan constituent and the group. This doesn't entail equating the two states of affairs as you seem to be inferring. Simultaneously, the single swan exists and the group of swans exist.
You don't have to accept the ontology, but at least understand that it comprises a coherent physicalist ontology - and Armstrong explicitly rejects Platonism. If it SEEMS incoherent to you, it's due to the brevity of my discussion.