create type second_max_int_state as (m int, pm int);

create or replace function second_max_sfunc(second_max_int_state, int)
returns second_max_int_state language sql as $$select
case
  when $ 1 .m is null then ($ 2 , null)::second_max_int_state
  when $ 1 .m<$ 2  then ($ 2 , $ 1 .m)::second_max_int_state
  when ($ 1 .pm<$ 2  or $ 1 .pm is null) and $ 1 .m>$ 2  then ($ 1 .m, $ 2 )::second_max_int_state
  else $ 1 
end
$$;

create or replace function second_max_ffunc(second_max_int_state)
returns int language sql as $$select $ 1 .pm$$;

create aggregate second_max (int) (
  SFUNC=second_max_sfunc, STYPE=second_max_int_state, FINALFUNC=second_max_ffunc
);

--test--
create temp table t as
select * from (values ( 1 , 1 ),( 2 , 20 ),( 1 , 2 ),( 1 , 3 ),( 1 , 4 ),( 2 , 5 ),( 2 ,- 1 ),( 3 , 0 ),( 2 , 20 )) v(a,b);

select a,b from t order by  1 , 2 ;

select a, max(b), second_max(b) from t group by a order by  1 ;