SQL Server SELECT into existing table

I am trying to select some fields from one table and insert them into an existing table from a stored procedure. Here is what I am trying:

SELECT col1, col2
INTO dbo.TableTwo 
FROM dbo.TableOne 
WHERE col3 LIKE @search_key

I think SELECT ... INTO ... is for temporary tables which is why I get an error that dbo.TableTwo already exists.

How can I insert multiple rows from dbo.TableOne into dbo.TableTwo?