"Under signatures" is a phrase that can refer to written documents that have been signed by the parties involved. Some possible synonyms for this phrase might include "with signatures," "signed by," or "bearing signatures." Other options could include "authored by," "endorsed by," or "validated by signatures." Depending on the context in which the phrase is used, some alternative phrases might be more appropriate than others. Nonetheless, it is important to remember that all of these phrases convey the same general meaning and indicate that the document in question has been formally signed, authenticated, or validated by the appropriate parties.