|Towards more picturesque speech™
In which one does not need the preposition “into” seeing as, by definition, entering something — even a legal contract — is “going into it”. Yet even stylists as fine as the draftsperson of A Manual of Style For the Drafting of Contractual Instruments — whose very title betrays its author as the sort of fellow whose idea of “style” is a waistcoat and pantaloons — find the thought of omitting that preposition oddly “unnatural”.
Nonetheless, the resourceful draftsperson will insist on entering into legal agreements (and might correct your draft if you neglect to do so). Indeed, one with a higher dan might even chain his or her prepositions together, tether them to a passive and speak reverently of a transaction “entered into under this agreement”.