When it comes to synonyms for the phrase "put down," there are several options available. One of the most common alternatives is "place," which is a simple and straightforward replacement that can be used in a variety of contexts. Another option is "depose," which is often used in more formal situations, such as political or legal contexts. "Lay down" is another alternative that works well in many instances, especially if you are discussing an item or object that needs to be set down carefully. Other options include "set down," "drop," and "deposit." Ultimately, the best synonym for "put down" will depend on the specific context in which it is being used.