We report on the design and performance of a novel nonreciprocal acoustic filter ( nrFIL) topology. This relies on the use of acoustic filters placed in switch-based angular-momentum-biased circuits and enabling orders-of-magnitude higher isolation levels than attained by previously reported nrFILs-prototypes. We show that by strategically adding modulated ad-hoc shunt filtering branches to a conventional nrFIL, it is possible to modify its dynamics, thus enabling orders-of-magnitude higher isolation within a large portion of its static passband. To prove the effectiveness of this approach, we first designed, simulated and built a conventional switch-based nrFIL based on three commercial 895 MHz acoustic filters placed in a star-circuit topology. Then, three ad-hoc time-modulated filtering branches were inserted between the central node of the built nrFIL and ground. All circuit branches relied on the same modulation frequency (38MHz) to work. We show how this modification allows to increase the isolation ( >25dB) attained by the conventional nrFIL prototype without degrading the minimum insertion loss attained in the passband of each acoustic filter ( IL ~ 6.5dB with or without the additional branches). Fractional bandwidth ( BW%), 1 dB-compression input power (P1dB) and IIP3 approaching 2.2%, 21.5 dBm and 41 dBm are reported.