Integrating ferroelectric thin films into the gate stack of high electron mobility transistors (HEMTs) would enable modulation of the threshold voltage (V_th) and, ultimately, switching between depletion (D)- and enhancement (E)-mode within the same HEMT. However, the experimental range over which V_th can be modulated is often substantially smaller than that expected from the coercive voltage. A comprehensive model for complete control over the interplay between ferroelectric switching and HEMT operation is presented, considering a versatile ferroelectric-metal-HEMT (FeMHEMT) configuration. The proposed model delivers quantitative predictions of achievable V_th values in relation to the ferroelectric polarization orientation, which are verified through a modular approach of connecting ferroelectric capacitors to metal-insulator-semiconductor (MIS) HEMTs. Essential guidelines for integrating wurtzite- and fluorite-structured ferroelectrics with HEMTs at their full potential are presented. The area ratio between the ferroelectric and MIS capacitors is identified as a crucial parameter for achieving complete polarization reversal without MIS breakdown, especially for wurtzite-structured ferroelectrics. Comparing hafnium zirconium oxide and aluminium scandium nitride, the role played by the charge injected into the floating gate on the FeMHEMT operation is elucidated. A remarkably large memory window of 37.6 V is experimentally demonstrated while switching between D- and E-mode within the same FeMHEMT.