The phrase "stay down" can convey a variety of meanings, from remaining in a prone position to avoiding participation in a confrontation. When looking for synonyms for this phrase, one option might be "keep low," which suggests staying out of sight or avoiding detection. Another possibility is "remain grounded," which highlights the importance of staying firmly rooted and not being easily swayed. Alternatively, "maintain a low profile" could imply a deliberate strategy of avoiding attention or conflict. Ultimately, the most appropriate synonym will depend on the specific context and intended meaning of the phrase "stay down".