Time-division multiplexing (TDM) of transition-edge-sensor (TES) microcalorimeters is being developed as the readout technology for the Athena X-ray integral field unit (X-IFU) and CMB-S4. We present an experimental demonstration of our latest TDM architecture, which has been implemented in a 4-column × 34-row chip that is fully compatible with the X-IFU design specifications. This new “mux21” architecture is designed for differential readout and uses two-layer switches to reduce the number of row-address lines while also incorporating changes that reduce power to roughly 40% and the total number of SQUIDs to half that of TDM chips used in previous publications. With the 160 ns row durations specified for X-IFU, we obtained (2.02 ± 0.03) eV FWHM energy resolution at 5.9 keV in 2-column × 34-row TDM readout of a NASA X-IFU-like TES array, which meets the requirements of X-IFU's energy-resolution budget. Finally, a scaling analysis of our improved TDM readout chain to bolometer applications indicates that multiplexing factors on the scale of several hundred are possible, depending on the readout requirements.