Opening a NY branch of a CA construction business
You can expand your business by registering your California company as a foreign entity in New York.
When filing a foreign entity, you do not need to get a new EIN, however you will need to obtain specific licensing on a state to state basis, such as a state contractor license.
Keep in mind when filing as a foreign entity in a different state you may have additional requirements to comply with depending on your original entity type. For example, LLC's established in New York as new or foreign entities are required to publish articles to the public regarding the business formation and purpose.