The ALTER TABLE command in SQL can perform various actions related to table structure and constraints. Three actions that can be performed using the ALTER TABLE command are: renaming a table, dropping all columns simultaneously from a table, and enabling or disabling constraints on a table. Renaming a table involves changing the name of the table within the database. Dropping all columns simultaneously implies removing multiple columns in one operation; however, typically this is limited to certain database systems and contexts, and often, dropping all columns equates to dropping the table itself. Enabling or disabling constraints involves modifying the rules enforced on the table data, such as primary keys, foreign keys, or unique constraints. These actions directly impact the table's schema and constraints, aligning with typical use cases for ALTER TABLE.