you'll want to use the GUI in SSMS;and change it to bigINT; the GUI will create a new table witht he proper structure, migrate the data, migrate all the foreign keys, constraints, etc, and drop teh old, then rename the new table to the proper name;

it is much easier and faster to use the GUI than to do that by hand, especially on a big busy table.

i'm fairly sure that it also changes the child tables that point to it with foreign keys, since they need to be changed to BIGINT also. one simple operation like changing the data type might affect dozens or hundreds of tables.

everyone will be locked out of the table while you are changing it, but they cannot insert right now, i would assume, so you are probably going to have to do this right away.