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We consider a type I or type X two Higgs doublets model with a modifiedlepton sector. The generalized lepton sector is also flavor conserving but withthe new Yukawa couplings completely decoupled from lepton mass proportionality.The model is one loop stable under renormalization group evolution and itallows to reproduce the $g-2$ muon anomaly together with the differentscenarios one can consider for the electron $g-2$ anomaly, related to theCesium and/or to the Rubidium recoil measurements of the fine structureconstant. Thorough parameter space analyses are performed to constrain all themodel parameters in the different scenarios, either including or not includingthe recent CDF measurement of the W boson mass. For light new scalars withmasses in the $0.2$-$1.0$ TeV range, the muon anomaly receives dominant oneloop contributions; it is for heavy new scalars with masses above $1.2$ TeVthat two loop Barr-Zee diagrams are needed. The electron $g-2$ anomaly, if any,must always be obtained with the two loop contributions. The final allowedregions are quite sensitive to the assumptions about perturbativity of Yukawacouplings, which influence unexpected observables like the allowed scalar massranges. On that respect, intermediate scalar masses, highly constrained bydirect LHC searches, are allowed provided that the new lepton Yukawa couplingsare fully scrutinized, including values up to 250 GeV. In the framework of acomplete model, fully numerically analysed, we show the implications of therecent $M_{W}$ measurement.

Muon and electron $g-2$ anomalies in a flavor conserving 2HDM with an oblique view on the CDF $M_W$ value