one thing or person after another
one after another
Consecutively and in quick succession, with one person or thing rapidly following another in order (and usually indicating a large amount altogether). (Often formulated as "one (noun) after another.") The children walked silently, one after another, into the schoolhouse to begin their lesson. When I was cooped up in the house after my surgery, I started reading one book after another.
one thing or person after another
a series of things or people that seems without limit. It's just one problem after another. One customer after another has been buying shoes today!