REGEXP_SUBSTR in Snowflake, regex that will extract the string after the period (which occurs between 0-2 times)

I'm trying to use the REGEXP_SUBSTR method in Snowflake to extract a string after the period. I have the following possibilities:

• ALTER TABLE DATABASE_NAME.SCHEMA_NAME.TABLE_NAME ADD COLUMN ....
• ALTER TABLE SCHEMA_NAME.TABLE_NAME ADD COLUMN ....
• ALTER TABLE TABLE_NAME ADD COLUMN ....

With the following possibilities, I need to be able to extract TABLE_NAME. So far, I've tried this which is able to get the third possibility:

select regexp_substr(query_text, 'ALTER TABLE ([0-9A-Za-z\\-\\_]+) ADD COLUMN', 1,1, 'e', 1);

I'm not sure how I could capture all three possibilities in one regular expression. Would appreciate any pointers. Thank you.

Using regexp and split_part:

WITH cte(query_text) AS (
   SELECT 'ALTER TABLE DATABASE_NAME.SCHEMA_NAME.TABLE_NAME ADD COLUMN ....' UNION
   SELECT 'ALTER TABLE SCHEMA_NAME.TABLE_NAME ADD COLUMN ....' UNION
   SELECT 'ALTER TABLE TABLE_NAME ADD COLUMN ....'
)
select 
  regexp_substr(query_text, 'ALTER TABLE (.+) ADD COLUMN', 1,1, 'e', 1) as obj_name,
  split_part(obj_name, '.', -1) AS tab_name,
  split_part(obj_name, '.', -2) AS schema_name,
  split_part(obj_name, '.', -3) AS db_name
FROM cte;

Output: