Postgres 9.6

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create table t(id serial primary key, rnd double precision);
with w as (insert into t(rnd) values(random()) returning *)
insert into t(rnd) select random() from w returning *;

id
rnd

2
0.219554797746241

with w as (insert into t(rnd) values(random()) returning *)
insert into t(rnd) select random() from w returning *, 1.0 dummy;

id
rnd
dummy

4
0.911946333944798
1.0

with w as (insert into t(rnd) values(random()) returning *)
insert into t(rnd) select random() from w returning *, w.rnd;
ERROR:  missing FROM-clause entry for table "w"
LINE 2: ...nsert into t(rnd) select random() from w returning *, w.rnd;
                                                                 ^