  We study the Electroweak symmetry breaking mechanism with extra Electroweak
symmetry breaking contributions (eEWSB) that are bounded by the Fermi constant
and limits from the related collider searches. The eEWSB is helpful to build a
different zero temperature vacuum structure from the Standard Model (SM), and
therefore leads to different Electroweak phase transition patterns at the early
Universe. We investigate the collider search prospects and gravitational waves
(GW) predictions from the strongly firstly order phase transition (SFOEWPT) in
this scenario. The Higgs pair searches at lepton colliders are found to be
complementary with the GW searches of the SFOEWPT parameter spaces.
