ALTER TABLE ... ENGINE=INNODB in one database blocks ALTER TABLE in other databases

I have 400 databases on my server. If I issue an ALTER TABLE ... ENGINE=INNODB on different tables in different databases at the same time, the updates are serialised - i.e only one ALTER TABLE is executed on the server at a time.

All other ALTER TABLE on unrelated tables in unrelated databases block with a status of "checking permissions".

I have about 28,000 tables / 400 databases / 250G of MyISAM. This serialisation means that it takes 6 hours to perform a MyISAM to INNODB upgrade. The server load and iostats indicate that the server is almost idle this entire time.