The　rapid　development　of　new　technologies,　e.g.,　connected　vehicles　and　e-wallet,　offers　us　opportunities　to　rethink　cooperative　lane-change　(LC)　models.　Most　of　existing　cooperative　LC　models　require　a　selfless　assumption　by　default,　which　is　usually　too　stringent　for　travelers.　A　cooperative　LC　game　framework　with　appropriate　side-payments　can　make　up　for　this　deficiency.　In　such　games,　when　travelers　maximize　their　own　benefits,　they　will　naturally　cooperate　to　improve　the　system　performance.　This　paper　designs　a　four-step　transferable　utility　based　three-player　game　framework,　which　can　cover　all　LC　scenarios　on　multi-lane　roads　combing　with　the　two-player　model　in　the　previous　work.　Our　four-step　framework　is　also　suitable　for　other　cooperative　games　with　side-payments.　Furthermore,　the　simulation　results　show　that,　cooperative　games　with　side-payments　can　reduce　vehicles＇　LC　frequency　and　meanwhile　benefit　all　transaction　vehicles　in　most　scenarios　in　expectation.　Moreover,　the　urgent　vehicles　with　very　high　values　of　time　can　save　up　to　42%　travel　time　on　congested　roads　under　the　simulation　settings.