When it comes to keeping things under control, there are various synonyms you can use for the phrase "clamping down on." For instance, you can use the expression "tightening one's grip on" to imply that you're trying to exert greater control over the situation. Similarly, you can use the phrase "cracking down on" to suggest that you're trying to become more severe or intense with the measures you're taking. Other words that can be used to replace "clamping down on" are "enforcing," "curbing," "restraining," and "suppressing." Each of these synonyms has its unique connotation and can be used depending on the context of the sentence.