You don't enrich *by*, but rather enrich *in*.

That is to say, we're starting with \\( \mathcal{V} := (V, \le, I, \otimes ) \\) first, and then we build a new kind of \\( \mathcal{V}\\)-category, called \\( \mathcal{X} \\), out of the appropriate \\( \mathcal{V}\\)-building blocks following certain constraints, if that makes sense.

That is to say, we're starting with \\( \mathcal{V} := (V, \le, I, \otimes ) \\) first, and then we build a new kind of \\( \mathcal{V}\\)-category, called \\( \mathcal{X} \\), out of the appropriate \\( \mathcal{V}\\)-building blocks following certain constraints, if that makes sense.