Lars, maybe that wasn't exactly what I meant to say, but what you wrote
is still correct.

Many people seem to think of digital samples as integer values. I tend
to think of them as binary fractions, and find that scheme more apt. So
when I talk about "adding more steps" I really mean the same thing as
"adding more decimal places" to a fractional number such as 3.14159...
-- the magnitude won't change significantly, but precision is improved
to the extent that the additional digits represent valid, actual data.

Certainly one can work in the other direction and imagine an integer
range which is extended, such that the noise floor (not quantization
noise, please--proper dither is an absolute requirement!) becomes less
and less when compared to the largest possible sample value. Either
way, as you say, more bits simply equals the capability for a wider
dynamic range.

--best regards