From G1909 (epi, upon) and G1299 (diatasso, to arrange/ordain). To add stipulations to an existing arrangement or covenant. Used only in Galatians 3:15, where Paul argues that no one can add conditions to a ratified covenant — including God's covenant with Abraham.
Paul's argument in Galatians 3:15 is devastatingly simple: even human covenants cannot be epidiatassomai-ed once ratified. How much more God's covenant with Abraham! The Mosaic Law, which came 430 years later, did not and could not add to or modify the Abrahamic promise. The theological implication is radical: salvation by grace through faith (the Abrahamic covenant) was never replaced or supplemented by works of the Law. The Law served a different purpose — as a tutor leading to Christ (Gal 3:24) — but it never altered the terms of God's original promise.