multiple INSERTs in single CTE pipeline - sql

Question

I have an input table that looks like this:
intput(code, persons)
'ID1', 'Pete Sampras,Ricky Martin,Albert Einstein'
'ID2', 'Georges Mikael, Diego Maradona'
I want to produce 3 output tables:
ids_table(idcode, code)
1, 'ID1'
2, 'ID2'
persons(idperson, FirstName, LastName)
1, 'Pete', 'Sampras'
2, 'Ricky', 'Martin'
3, 'Albert', 'Einstein'
4, 'Georges', 'Mikael'
5, 'Diego', 'Maradona'
code_persons(idcode, idperson)
1, 1
1, 2
1, 3
2, 4
2, 5
I am using a pipeline of CTEs to do this. I was wondering if you could do multiple inserts in the same CTE pipeline. Something like:
WITH cte AS (
SELECT code, [value] AS person
FROM input
CROSS APPLY STRING_SPLIT(persons, ',')
), cte2 AS (
SELECT code, person, CHARINDEX(' ',person) AS splitIndex
FROM cte
), cte3 AS (
SELECT code, person, LEFT(person, splitIndex) AS FirstName,
SUBSTRING(person, splitIndex, 100) AS LastName
FROM cte2
), cte4 AS (
INSERT INTO ids_table(code)
SELECT DISTINCT code
FROM cte3
), cte5 AS (
INSERT INTO persons(FirstName, LastName)
SELECT FirstName, LastName
FROM cte3
), cte6 AS (
INSERT INTO code_persons(idcode, idpersons)
SELECT it.idcode, p.idperson
FROM cte3
JOIN persons p ON p.FirstName = cte3.FirstName AND p.LastName=cte3.LastName
JOIN ids_table it ON cte3.code=it.code
)
--Some code to trigger execution
One solution I can think of is to store the output of cte3 into a temporary table.
Is there a way to avoid this ?