Alternative phrases that can be used as synonyms for the term "at the sacrifice of" include the phrases "at the expense of," "at the cost of," or "in detriment to." By using these phrases, the author is indicating that there are negative consequences to the action being taken. Such phrases are commonly used when discussing trade-offs, where a particular action or decision may benefit one party while detracting from another. It is crucial to consider the potential downsides of any decision made and the impact it may have on all parties involved, which can be clearly conveyed by using synonyms for "at the sacrifice of".