Roman numerals do not name literal chords. They label chord functions. As such, the appropriate Roman numeral would depend on the context: the chords both before and after. An E♭ major chord appearing in the key of C could be a borrowed chord from minor, an applied chord in some other key, a modulation/tonicization in itself, or a passing/ornamental chord that wouldn't receive a Roman numeral.
The further complication is that it depends on the "in between" chord. E♭ minor, augmented, and diminished — not to mention the various seventh chords rooted on E♭ — would also be "in between" chords subject to the same context-dependency described above.
In fact, even the idea that D minor is
ii, for example, makes quite a few assumptions about context. It would be somewhat more accurate to say "In the key of C major, a D minor chord commonly functions as a