No. We cannot alter the constraint, only thing we can do is drop and recreate it
ALTER TABLE [TABLENAME] DROP CONSTRAINT [CONSTRAINTNAME]
Foreign Key Constraint
Alter Table Table1 Add Constraint [CONSTRAINTNAME] Foreign Key (Column) References Table2 (Column) On Update Cascade On Delete Cascade
Primary Key constraint
Alter Table Table add constraint [Primary Key] Primary key(Column1,Column2,.....)