Trying to include "Blank Cells" in a SUMIFS formula

All arguments in SUMIFS() work like AND, not OR. Hard to say for sure without seeing a sample WB, but perhaps add 2 SUMIFS() together, or use something like...
=SUM(SUMIF(sum range, criteria range ,{"criteria1","Criteria1"}))
You may not need the "" if your criteria is numeric

If that doesn't work, upload a small (clean) sample workbook (not a pic) of what you are working with, and what your expected outcome would look like.

The problem is, I can't use "" to refer to empty cells in a SUMIFS fonction, given the syntax of the formula. And I tried to come up with something with either OR, AND or ISBLANK, but can't figure out how to make it work.

The file is attached to this message. The formula in question is in cell E8.

First two argument of the SUMIFS fonction are:
- IF Date in column G is higher or equal to the date in 'HIDDEN CODES' cell E32.
- IF Date in column G is lower or equal to the date in 'HIDDEN CODES' cell E33.

This gives me a specific array of transaction to look into. This is where it gets tricky. From this array, I need to SUM the profits (Column M) of every transaction that has closing date (Column K) higher the ending date ('HIDDEN CODES' cell E33) AND possible transactions that haven't been closed yet (Empty cells in Column K), but only within the array previously delimited by the first two arguments.

If you take a look at the file attached to this message, the correct dates have been entered...and E8 should return a sum of 270. Which is the +$6,320 in M82 (which is taken into account right now, because it has a closing date)...but it doesn't add the ones without a closing date (M81, M83, M84 and M85), which should be counted since it's within the array delimited by the first two arguments.

Basically, in an ideal world, the formula would look something like this (key part in bold):

=SUMIFS(CARNETJDV[[#All],[VNTPROF]],CARNETJDV[[#All],[ACHDATE]],">="&'HIDDEN CODES'!$E$32,CARNETJDV[[#All],[ACHDATE]],"<="&'HIDDEN CODES'!$E$33,CARNETJDV[[#All],[VNTDATE]],OR(">"&'HIDDEN CODES'!$E$33,"="&""""))

or

=SUMIFS(CARNETJDV[[#All],[VNTPROF]],CARNETJDV[[#All],[ACHDATE]],">="&'HIDDEN CODES'!$E$32,CARNETJDV[[#All],[ACHDATE]],"<="&'HIDDEN CODES'!$E$33,OR(CARNETJDV[[#All],[VNTDATE]]>'HIDDEN CODES'!$E$33,CARNETJDV[[#All],[VNTDATE]]=""))

1. Your "dates" in Hidden Codes are text, not dates. Change that formula to this...
=IF(ISBLANK(CARNET!$C$5),DATE(1900,1,1),CARNET!$C$5)

2. your formula...
=SUMIFS(CARNET!$M$23:$M$85,
CARNET!$G$23:$G$85,">="&'HIDDEN CODES'!$E$32,
CARNET!$G$23:$G$85,"<="&'HIDDEN CODES'!$E$33,
CARNET!$K$23:$K$85,">"&'HIDDEN CODES'!$E$33)
if you look at the last rule, you are looking for all entries later than E33 - no records match that

Try this...
=SUMIFS(CARNET!$M$23:$M$85,
CARNET!$G$23:$G$85,">="&'HIDDEN CODES'!$E$32,
CARNET!$G$23:$G$85,"<="&'HIDDEN CODES'!$E$33,
CARNET!$K$23:$K$85,"")