Recognising categories of enriched categories

Given a monoidal category $$\mathcal V$$ one has the category $$\mathcal V{-}\mathbf {Cat}$$ of (small) $$\mathcal V$$-enriched categories and $$\mathcal V$$-enriched functors (and $$\mathcal V$$-enriched natural transformation if one wishes to obtain a $$2$$-category). Starting with an arbitrary category $$\mathscr C$$ are there known conditions that guarantee that $$\mathscr C$$ is equivalent to $$\mathcal V$$-$$\mathbf {Cat}$$ for some $$\mathcal V$$? Are there effective ways of showing that $$\mathscr C$$ is not equivalent to $$\mathcal V$$-$$\mathbf {Cat}$$ for all $$\mathcal V$$?