When it comes to staking out, there are a number of synonyms that can be used interchangeably. If you're looking to stake out a claim, you may also use words such as "established," "secured," or "identified." Alternatively, if you're referring to the act of keeping an eye on something, you might choose to use synonyms like "observed," "watched," or "monitored." In some cases, "patrolled," "guarded," or "surveilled" might also be appropriate. Essentially, any word that implies a level of vigilance or ownership can be used as a synonym for staking out to convey the intended message.