at the expense of sb/sth
with loss or damage to sb/sth 在牺牲(或损害)…的情况下
He built up the business at the expense of his health.

5[PHRASE 短语] 以牺牲…的利益为代价;If you achieve something at the expense of someone, you do it in a way which might cause them some harm or disadvantage. [PHR after v]
But skeptics worry that costs may be trimmed at the expense of the patient…
但是持怀疑态度的人担心费用的削减会以牺牲病人的利益为代价。
According to this study, women have made notable gains at the expense of men.
根据这项研究,女性以牺牲男性的利益为代价而获得了显著的收益。

6[PHRASE 短语] 以…为代价;If you say that someone does something at the expense of another thing, you are expressing concern at the fact that they are not doing the second thing, because the first thing uses all their resources. [PHR after v] [disapproval]
They are worth having but not at the expense of better services…
它们值得拥有,但是不能因此放弃更好的服务。
The orchestra has more discipline now, but at the expense of spirit.
那个管弦乐团现在更有纪律性了,却丧失了灵魂。