We propose and investigate experimentally an interferometrically stable, polarization-selective pulse multiplexing scheme for direct laser amplification of picosecond pulses. The basic building block of this scheme is a Sagnac loop which allows for a straightforward scaling of the pulse-multiplexing scheme. Switching the amplifier from single-pulse amplification to burst mode increases extraction efficiency, reduces parasitic non-linearities in the gain medium and allows for higher output energies. Time-frequency analysis of the amplified output pulses demonstrates the viability of this approach.