How to select mutiple values with like clause
This case is a good candidate for using REGEXP instead of LIKE.

SELECT * 
from table 
WHERE column REGEXP '^(AAA|BBB|CCC)'


REGEXP is case insensitive. For case sensitive searches use REGEXP BINARY.

SELECT * 
from table 
WHERE column REGEXP BINARY '^(AAA|BBB|CCC)'


REGEXP can't benefit from indexes, so it may only be an efficient option if LIKE wouldn't use indexes either. With multiple LIKE statements that could individually access an index (like in your case if column is indexed and the like has a wildcard at the end), performing UNION of individual queries with a single LIKE would probably be most effective in a large dataset.

However, if your query filter primarily by, say, a range of dates, then a single REGEXP may be faster than multiple LIKEs ORed.

For more information about REGEXP in MySQL see this and this.