at the expense of

preposition4

1. •
   Paid for by an individual or group.
2. •
   (figurative) In a way as to harm somebody or something; to the detriment of.

   • Bengali, like other Aryan languages of India, has spread, and is still spreading, at the expense of the aboriginal tongues. — 1926
3. •
   (figurative) Of a joke, deriding someone.
4. •
   At one's responsibility.