Postgres 12

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 create table DEMO1(n integer);

CREATE TABLE

 create table DEMO2(n integer);

CREATE TABLE

insert into DEMO1 values(42);

INSERT 0 1

alter table DEMO1 add unique(n); 

ALTER TABLE

select * from DEMO1;

n

42

SELECT 1

select * from DEMO2;

n

SELECT 0

do $$
begin
 insert into DEMO1 (n)  values (1);
 insert into DEMO1 (n)  values (42);
exception when others then 
 insert into DEMO2 select * from DEMO1;
end;
$$ language plpgsql;

DO

select * from DEMO2;

n

42

SELECT 1