There are several synonyms for the phrase "on certain conditions," including "contingent upon," "provided that," "subject to," "conditional on," and "under the condition that." All of these expressions convey the idea that something is possible or allowable only if specific requirements are met. Depending on the context, one of these phrases may be preferred over the others. For example, "contingent upon" suggests a more conditional or uncertain state of affairs than "provided that," which implies a more solid or reliable agreement. Choosing the right synonym can help clarify the conditions under which a particular action or decision can be made.