Yes, Just set the enabled or locked property of the field based on the user
who is logged on.
Do this in code when the form is opened.
Make sure the form is based on a query set to run with owner's permissions.
Also make sure your other users have no access to the underlying table or
query. If you don't then they can just go around you and disregard your
code.
Another common practice would be to lock all the fields once a certain item
was checked. In your example, once the CEO has signed off, you may want to
write similar code that locks all the fields on the form as long as there is
an entry in the date field you mention. This would basically lock the
record once the CEO did their thing. This code would have to look at each
record, not just once when the form is opened. To accomplish this, you'd
have to tie this code to the form's "current" event. This even fires every
time the user moves to a different record. So, as they scroll through
records, the fields would become enabled or disabled depending on the date
field.