You can create partial keys on multiple columns.
mysql>
mysql> CREATE TABLE Employee(
-> id int,
-> first_name VARCHAR(15),
-> last_name VARCHAR(15),
-> start_date DATE,
-> end_date DATE,
-> salary FLOAT(8,2),
-> city VARCHAR(10),
-> description VARCHAR(15)
-> );
Query OK, 0 rows affected (0.02 sec)
mysql>
mysql> insert into Employee(id,first_name, last_name, start_date, end_Date, salary, City, Description)
-> values (1,'Jason', 'Martin', '19960725', '20060725', 1234.56, 'Toronto', 'Programmer');
Query OK, 1 row affected (0.00 sec)
mysql>
mysql> insert into Employee(id,first_name, last_name, start_date, end_Date, salary, City, Description)
-> values(2,'Alison', 'Mathews', '19760321', '19860221', 6661.78, 'Vancouver','Tester');
Query OK, 1 row affected (0.01 sec)
mysql>
mysql> insert into Employee(id,first_name, last_name, start_date, end_Date, salary, City, Description)
-> values(3,'James', 'Smith', '19781212', '19900315', 6544.78, 'Vancouver','Tester');
Query OK, 1 row affected (0.00 sec)
mysql>
mysql> insert into Employee(id,first_name, last_name, start_date, end_Date, salary, City, Description)
-> values(4,'Celia', 'Rice', '19821024', '19990421', 2344.78, 'Vancouver','Manager');
Query OK, 1 row affected (0.00 sec)
mysql>
mysql> insert into Employee(id,first_name, last_name, start_date, end_Date, salary, City, Description)
-> values(5,'Robert', 'Black', '19840115', '19980808', 2334.78, 'Vancouver','Tester');
Query OK, 1 row affected (0.00 sec)
mysql>
mysql> insert into Employee(id,first_name, last_name, start_date, end_Date, salary, City, Description)
-> values(6,'Linda', 'Green', '19870730', '19960104', 4322.78,'New York', 'Tester');
Query OK, 1 row affected (0.02 sec)
mysql>
mysql> insert into Employee(id,first_name, last_name, start_date, end_Date, salary, City, Description)
-> values(7,'David', 'Larry', '19901231', '19980212', 7897.78,'New York', 'Manager');
Query OK, 1 row affected (0.00 sec)
mysql>
mysql> insert into Employee(id,first_name, last_name, start_date, end_Date, salary, City, Description)
-> values(8,'James', 'Cat', '19960917', '20020415', 1232.78,'Vancouver', 'Tester');
Query OK, 1 row affected (0.00 sec)
mysql>
mysql> select * from Employee;
+------+------------+-----------+------------+------------+---------+-----------+-------------+
| id | first_name | last_name | start_date | end_date | salary | city | description |
+------+------------+-----------+------------+------------+---------+-----------+-------------+
| 1 | Jason | Martin | 1996-07-25 | 2006-07-25 | 1234.56 | Toronto | Programmer |
| 2 | Alison | Mathews | 1976-03-21 | 1986-02-21 | 6661.78 | Vancouver | Tester |
| 3 | James | Smith | 1978-12-12 | 1990-03-15 | 6544.78 | Vancouver | Tester |
| 4 | Celia | Rice | 1982-10-24 | 1999-04-21 | 2344.78 | Vancouver | Manager |
| 5 | Robert | Black | 1984-01-15 | 1998-08-08 | 2334.78 | Vancouver | Tester |
| 6 | Linda | Green | 1987-07-30 | 1996-01-04 | 4322.78 | New York | Tester |
| 7 | David | Larry | 1990-12-31 | 1998-02-12 | 7897.78 | New York | Manager |
| 8 | James | Cat | 1996-09-17 | 2002-04-15 | 1232.78 | Vancouver | Tester |
+------+------------+-----------+------------+------------+---------+-----------+-------------+
8 rows in set (0.00 sec)
mysql>
mysql> ALTER TABLE Employee ADD KEY comp_index (last_name(6),city(2),description(3));
Query OK, 8 rows affected (0.03 sec)
Records: 8 Duplicates: 0 Warnings: 0
mysql>
mysql> show keys from Employee;
+----------+------------+------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
| Table | Non_unique | Key_name | Seq_in_index | Column_name | Collation | Cardinality | Sub_part | Packed | Null | Index_type | Comment |
+----------+------------+------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
| Employee | 1 | comp_index | 1 | last_name | A | NULL | 6 | NULL | YES | BTREE | |
| Employee | 1 | comp_index | 2 | city | A | NULL | 2 | NULL | YES | BTREE | |
| Employee | 1 | comp_index | 3 | description | A | NULL | 3 | NULL | YES | BTREE | |
+----------+------------+------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
3 rows in set (0.00 sec)
mysql>
mysql> drop table Employee;
Query OK, 0 rows affected (0.00 sec)
mysql>