In this contribution, we present a preliminary assessment of the capabilities of electronically steerable transmitarray antennas (TAs) for Ka-band satellite communications, with emphasis on SatCom-on-the-move (SOTM) up-link terminals. These studies build on a novel linearly-polarized four-state (2-bit) unit cell (UC) comprising four p-i-n diodes. The enhanced phase resolution allows one to increase the directivity by 2.5 dB with respect to state-of-the-art 1-bit TA designs and to reduce the sidelobe levels (SLLs). Several configurations based on a 50 \times 50- element transmitarray are analyzed to show the design trade-offs in terms of gain, bandwidth, scanning performance and antenna size, in the case of linear polarization. The achieved gain patterns are also compared to stringent radiation envelopes defined by regulations for SOTM. Switchable circular polarization is demonstrated combining two sets of unit cells radiating orthogonal linear polarizations. In this case, as per simulations, the -3-dB gain bandwidth spans from 28 GHz to 31 GHz, with peak gain of 31.3 dBiC at broadside. © 2020 EurAAP.