Enforcing adjacent ranges

I'm wondering if there is anyway to enforce that ranges in a table be
adjacent in perhaps a similar way to enforcing that they are
non-overlapping.

Consider a (very simplified table)

CREATE TABLE (
thing_id int,
period tsrange,
EXCLUDE USING gist (thing_id WITH =, period WITH &&),
CHECK (lower_inc(period) and not upper_inc(period))
);

This should (I believe) enforce that all periods for a given thing are
non-overlapping, and that each is lower-inclusive, upper-exclusive ranges.

I'd also like to enforce that all ranges for a given 'thing' are adjacent.

Is that possible?

Thanks,

Ben