I have a table with column ID that is identity one. Next I create new non-identity column new_ID and update it with values from ID column + 1. Like this:
new_ID
An Identity is a property that is set at the time the table is created or a new column is added in alter table statement. You can't alter the column and set it to identity and it is impossible to have two identity columns within the same table.
Depending on the size of the table, is it possible to simply create a new table? copy over the schema of the old one and then use SET IDENTITY_INSERT ON to populate the new identity column with what you want from the old one.