EOMONTH Algorithm? - excel

Question

I need to recreate some of the functionality from Excel's EOMONTH function -- specifically the ability to enter a date and an integer representing a number of months in the future or past, and from those inputs calculate a new date that is the last day of the target month. I have been using Excel formulas for some simple testing and I can get close but cannot get it exactly right. So I would like to do this in Excel but without using the EOMONTH function or any of the other fancy date-related functions like EDATE or DATE or similar (because some of these automatically handle / correct some kinds of invalid data ... like months larger than 12 for example). TRUNC and MOD are fine ... and basic math operators ... but that's about it. This needs to be done in excel only -- no VBA code. We can assume the date entered is a month-end date, if that helps.
Say I have the following data in cells:
A1: 12/31/2021
A2: 1
The result in A3 or wherever should be 1/31/2022
With A1: 12/31/2021
A2: 0
A3 should be 12/31/21
A1: 12/31/2021
A2: -1
A3 should be 11/30/2021
A1: 12/31/2021
A2: -12
A3 should be 12/31/2020
I need to go up to 60 months forward or backward from any valid end-of-month date. I have been able to do what I want with a positive number (or zero) in A2, but negative numbers cause issues which I have not been able to figure out. I am using MOD + TRUNC + some basic math inside IF statements -- pretty ugly and doesn't handle negative numbers so I'm hoping there is a better way. Oh ... and I have actually been deriving Day 1 of the month following my "target month" ... and then subtracting 1 from that Day 1 date, to arrive at my target End Of Month date. This seems to me like a good way to work around the (lack of) EOMONTH function ... but I am happy to entertain any and all ideas / options.
--- New Info added 12/23 ---
I cannot simply use the EOMONTH formula because my target language (a virtual attribute in Uniquery) does not support it. So I am prototyping the solution in Excel but will implement it in the other system.
I did not include the detail below initially because A) I think there must be a more elegant solution so I am a little embarrassed about this ugliness and B) it is a lot of detail which I thought might be unnecessary. But since you asked :) here is some data from my worksheet showing what I have done and the results (and the issue).
Input:
A3 (input date): 10/15/2020
E3 (Months +/-): *** see comments below ***
Formulas:
B3 (input month): =MONTH(A3)
D3 (input Year): =YEAR(A3)
G3 (Interim New Month): =B3+E3+1 (+1 to give me the month AFTER my target month)
H3 (Month Adjustment): =MOD(G3,12)
I3 (Year Adjustment): =TRUNC(G3/12,0)
J3 (New Month): =IF(H3=0,12,H3)
K3 (New Year): =IF(H3=0,D3+I3-1,D3+I3)
L3 (Interim New Date): =J3&"/1/"&K3 (This will be day after my target date)
M3 (New / Target Date): DATEVALUE(L3)-1
With a couple dozen dates in cells A3:A27, first date = 10/15/2020, second date = 11/15/202, etc. (each date in the following month) ... and the formulas above entered on row 3 then copy/pasted down to row 27 ... and trying various values in cell E3 ... I can see the formulas work for numbers from -2 up through +60, but fail for certain months when E3 contains -3 or smaller. Specifically, with E3=-3 and input date = 1/15/21 my logic fails because the Interim New Month (column G) calculates a value of -1 which causes problems for the downstream formulas. I have addressed some of these problems with the MOD and TRUNC logic ... and the IF H3=0 logic ... but the one thing I cannot figure out is how to get the year right. With the current formulas when E3 is -3 and the base date is 1/15/21 the final year comes out 2021 which is incorrect. It should be 2020. And when E3 = -4 the base dates of 1/15/21 and 2/15/21 both produce incorrect values for Year -- 2021 instead of 2020. Smaller and Smaller E3 values produce more incorrect results.
Surely there is a relatively easy solution to this but I just cannot see it!?!?
Thanks!