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.
See also: after, another, one
Farlex Dictionary of Idioms.

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!
See also: after, another, one, person, thing
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.
See also:
  • cooking for one
  • drive (one) out of office
  • force (one) out of office
  • force out of office
  • except for one thing
  • give (one) (one's) head
  • give head
  • give somebody their head
  • give someone their head