Integrated circuit packages with multiple integrated circuit dies are provided. A multichip package may include a substrate, a main die that is mounted on the substrate, and multiple transceiver daughter dies that are mounted on the substrate and that are coupled to the main die via corresponding Embedded Multi-die Interconnect Bridge (EMIB) interconnects formed in the substrate. Each of the main die and the daughter dies may include configurable adapter circuitry for interfacing with the EMIB interconnects. The adapter circuitry may include FIFO buffer circuits operable in a 1x mode or 2x mode and configurable in a phase-compensation mode, a clock-compensation mode, an elastic mode, and a register bypass mode to help support a variety of communications protocols with different data width and clocking requirements. The adapter circuitry may also include boundary alignment circuitry for reconstructing (de)compressed data streams.