[database] Can I have multiple primary keys in a single table?

This is the answer for both the main question and for @Kalmi's question of

What would be the point of having multiple auto-generating columns?

This code below has a composite primary key. One of its columns is auto-incremented. This will work only in MyISAM. InnoDB will generate an error "ERROR 1075 (42000): Incorrect table definition; there can be only one auto column and it must be defined as a key".

DROP TABLE IF EXISTS `test`.`animals`;
CREATE TABLE  `test`.`animals` (
  `grp` char(30) NOT NULL,
  `id` mediumint(9) NOT NULL AUTO_INCREMENT,
  `name` char(30) NOT NULL,
  PRIMARY KEY (`grp`,`id`)
) ENGINE=MyISAM;

INSERT INTO animals (grp,name) VALUES
    ('mammal','dog'),('mammal','cat'),
    ('bird','penguin'),('fish','lax'),('mammal','whale'),
    ('bird','ostrich');

SELECT * FROM animals ORDER BY grp,id;

Which returns:

+--------+----+---------+
| grp    | id | name    |
+--------+----+---------+
| fish   |  1 | lax     |
| mammal |  1 | dog     |
| mammal |  2 | cat     |
| mammal |  3 | whale   |
| bird   |  1 | penguin |
| bird   |  2 | ostrich |
+--------+----+---------+

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