I suppose you could route calls through multiple embedded auto attendants, no greetings, and selector codes nested to the next AA and the final AA transfers to the Conference Meet Me shortcode.
Main AA - Press 9 for Conference Bridge - Selector Code 9 transfer to AA-PIN-A
AA-PIN-A - recording says "Enter PIN" - ("PIN" is 1234) - Selector Code 1 transfers to AA-PIN-B
AA-PIN-B - No recording - Selector Code 2 transfers to AA-PIN-C
AA-PIN-C - No Recording - Selector Code 3 transfers to AA-PIN-D
AA-PIN-D - No Recording - Selector Code 4 transfers to Conference Meet Me shortcode