Yes, that is possible, you can connect the quad midi iic board to the J4A IIC port and still use one MBHP_MIDI_IO module to gain two base MIDI INs/OUTs (connect this board to J11E).
(I´ve 3 base MIDI outs on an old STM32 board SEQV4, and 4 IIC outs, it is great, so many MIDI cables! :-))
Many greets,
Peter