SQL Server JSON_Modify, How to Update all?

Here are two options. Disclaimer: I am not a pro at JSON through sql server 2016, but I have hacked some stuff together.

Option 1: You are clearly creating a result set from the JSON string. Why not create the result set and then update it?

DECLARE @jsontable TABLE (A varchar(50), b varchar(50), c varchar(50))
DECLARE @JSON NVARCHAR(MAX)

SET @JSON = 
N'{
"A":1,
"TMP": [    
    {"A":"VALUE1", "B": "VALUE2", "C": 1},
    {"A":"VALUE3", "B": "VALUE4", "C": 2},
    {"A":"VALUE5", "B": "VALUE6", "C": 3}]}
'

--SET @JSON = JSON_MODIFY(@JSON, '$.TMP.A', 'JEJE')
INSERT INTO @jsontable (a,b,c)
SELECT * FROM OPENJSON(@JSON, '$.TMP') WITH ( A NCHAR(10), B NCHAR(10), C INT )

UPDATE @jsontable 
SET a = 'JEJE' 

SELECT * 
FROM @jsontable

Option 2: you can manipulate the JSON components, but you have to pass the index to the function.

DECLARE @JSON NVARCHAR(MAX)
SET @JSON = 
N'{
"A":1,
"TMP": [    
    {"A":"VALUE1", "B": "VALUE2", "C": 1},
    {"A":"VALUE3", "B": "VALUE4", "C": 2},
    {"A":"VALUE5", "B": "VALUE6", "C": 3}]}
'

SET @JSON = JSON_MODIFY(@JSON, '$.TMP[0].A', 'JEJE')
SET @JSON = JSON_MODIFY(@JSON, '$.TMP[1].A', 'JEJE')
SET @JSON = JSON_MODIFY(@JSON, '$.TMP[2].A', 'JEJE')

SELECT * FROM OPENJSON(@JSON, '$.TMP') WITH ( A NCHAR(10), B NCHAR(10), C INT )