MySQL5.6不支持一个表有多个UPDATE/DELETE/INSERT触发器。
下边看一个例子：
创建三个测试表：

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mysql> create table t_trig_test_01 (name varchar(10));
Query OK, 0 rows affected (0.07 sec)

mysql> create table t_trig_test_02 (name varchar(10));
Query OK, 0 rows affected (0.03 sec)

mysql> create table t_trig_test_03 (name varchar(10));
Query OK, 0 rows affected (0.03 sec) 创建两个触发器：

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mysql> delimiter //
mysql> create trigger trg_test_01
-> after insert on t_trig_test_01
-> for each row
-> begin
-> insert into t_trig_test_02 select * from t_trig_test_01;
-> end;
-> //
Query OK, 0 rows affected (0.06 sec)

mysql> delimiter //
mysql> create trigger trg_test_02
-> after insert on t_trig_test_01
-> for each row
-> begin
-> insert into t_trig_test_03 select * from t_trig_test_01;
-> end;
-> //
Query OK, 0 rows affected (0.11 sec)向表t_trig_test_01插入两条测试数据：

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mysql> insert into t_trig_test_01 values('steven');
Query OK, 1 row affected (0.01 sec)

mysql> insert into t_trig_test_01 values('steven');
Query OK, 1 row affected (0.01 sec)查看三个表的数据：

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mysql> select * from t_trig_test_01;
+--------+
| name |
+--------+
| steven |
| steven |
+--------+
2 rows in set (0.00 sec)

mysql> select * from t_trig_test_02;
+--------+
| name |
+--------+
| steven |
| steven |
| steven |
+--------+
3 rows in set (0.00 sec)

mysql> select * from t_trig_test_03;
+--------+
| name |
+--------+
| steven |
| steven |
| steven |
+--------+
3 rows in set (0.00 sec) 达到了预期的结果。