On the bundle-of-universals theory of ordinary concrete particulars, such a particular is a bundle of its properties and its properties are universals. This theory will appeal to those who, for various ontological and epistemological reasons, resist substratum theories and think of properties as universals. Empiricists like Bertrand Russell, for example. Powerful objections can be brought against the theory, but the following two questions suggested by some comments of Peter Lupu in an earlier thread are, I think, easily answered.
Q1. How may universals does it take to constitute a particular? Could there be a particular composed of only one or only two universals?
Q2. We speak of particulars exemplifying properties. But if a particular is a bundle of its properties, what could it mean to say of a particular that it exemplifies a property?
A1. The answer is that it takes a complete set. I take it to be a datum that the ordinary meso-particulars of Sellars' Manifest Image -- let's stick with these -- are completely determinate or complete in the following sense:
D1. X is complete =df for any predicate P, either x satisfies P or x satisfies the complement of P.
If predicates express properties, and properties are universals, and ordinary particulars are bundles of properties, then for each such particular there must be a complete set of universals. For example, there cannot be a red rubber ball that has as constituents exactly three universals: being red, being made of rubber, being round. For it must also have a determinate size, a determinate spatiotemporal location, and so on. It has to be such that it is either covered with Fido's saliva or not so distinguished. If it is red, then it must have a color; if it is round, it must have a shape, and so on. This brings in further universals. Whatever is, is complete. That is a law of metaphysics, I should think. Or perhaps it is only a law of phenomenological ontology, a law of the denizens of the Manifest Image. (Let's not get into quantum mechanics.)
A2. If a particular is a bundle of universals, then it is a whole of parts, the universals being the (proper) parts, though not quite in the sense of classical mereology. Why do I say that? Well, suppose you have a complete set of universals, and suppose further that they are logically and nomologically compossible. It doesn't follow that they form a bundle. But it does follow, by Unrestricted Summation, that there is a classical mereological sum of the universals. So the bundle is not a sum. Something more is required, namely, the contingent bundling to make of the universals a bundle, and thus a particular.
Now on a scheme like this there is no exemplification (EX) strictly speaking. EX is an asymmetrical relation -- or relational tie: If x exemplifies P-ness, then it is not the case that P-ness exemplifies x. Bundling is not exemplification because bundling is symmetrical: if U1 is bundled with U2, then U2 is bundled with U1. So what do we mean when we say of a particular construed as a bundle that is has -- or 'exemplifies' or 'instantiates' using these terms loosely -- a property? We mean that it has the property as a 'part.' Not as a spatial or temporal part, but as an ontological part. Thus:
D2. Bundle B has the property P-ness =df P=ness is an ontological 'part' of B.
Does this scheme bring problems in its train? Of course! They are for me to know and for you to figure out.