mysqld_multi 設定方法

問題

mysqld_multiを使って一つのサーバのなかで複数のmysqlプロセスを設定したいと思っています。

mysqld_multi ドキュメント:
https://dev.mysql.com/doc/refman/5.7/en/mysqld-multi.html

ですが設定ファイルを置いてコマンドを叩いても、以下のエラーが出てしまいます。

[hoge@instance-1 tmp]$ sudo -u mysql mysqld_multi start 2
WARNING: Log file disabled. Maybe directory or file isn't writable?
mysqld_multi log file version 2.16; run: 木  8月 16 03:19:26 2018

Starting MySQL servers


Installing new database in /var/lib/mysql2


FATAL ERROR: Tried to start mysqld under group [mysqld2],
but no data directory was found or could be created.
data directory used: /var/lib/mysql2

# my.cnf

[mysqld_multi]
mysqld     = /usr/bin/mysqld_safe
mysqladmin = /usr/bin/mysqladmin
user       = multi_admin
password   = my_password

[mysqld2]
socket     = /var/lib/mysql/mysql.sock2
port       = 3307
pid-file   = /var/run/mysql2/mysqld.pid2
datadir    = /var/lib/mysql2
language   = /usr/share/mysql/mysql/english
user       = unix_user1

[mysqld3]
mysqld     = /path/to/mysqld_safe
ledir      = /path/to/mysqld-binary/
mysqladmin = /path/to/mysqladmin
socket     = /tmp/mysql.sock3
port       = 3308
pid-file   = /var/lib/mysql3/hostname.pid3
datadir    = /var/lib/mysql3
language   = /usr/share/mysql/mysql/swedish
user       = unix_user2

試したこと

ディレクトリの権限見直し

/var/lib/mysql2:
合計 8
drwxr-xr-x.  2 mysql mysql 4096  8月 16 02:24 2018 .
drwxr-xr-x. 28 root  root  4096  8月 16 02:33 2018 ..

mysqld ---initialized コマンド

エラーが出て終了

2018-08-16T02:24:19.247443Z 0 [Warning] TIMESTAMP with implicit DEFAULT value is deprecated. Please use --explicit_defaults_for_timestamp server option (see documentation for more details).
2018-08-16T02:24:19.249136Z 0 [ERROR] --initialize specified but the data directory has files in it. Aborting.
2018-08-16T02:24:19.249180Z 0 [ERROR] Aborting