Anything without a suffix was GSWR origin, or built new by the GSR or CIE. Oddball ones were more along the lines of those you mention, Minister. Nothing of GSWR origin acquired a suffix while in traffic, but if withdrawn and placed into departmental service, both GSWR and "suffixed" stock (of other companies) would have acquired an "A" suffix and also a completely new number. Thus, for a fictitious example, we might have GSWR coach no. 123, DSER coach no. 17 and ex-MGWR coach 42. After 1925, 123 stays as 123, while 42 becomes 42M. DSER 17 is now 17D.
Fast forward to 1959 and all three are withdrawn. The first two are stripped of seats and made into tool vans. A month previously, some other PW vehicle has been numbered 200A. Now, 123 and 42M become 201A and 202A.
Later, Inchicore builds another gadget, numbering it 203A, and then they decide they want the old DSER 17D as well. So it becomes 204A.
If you look at several preserved vehicles, most notably the two MGWR six wheelers on the DCDR, or the one at Clifden, or the one at Whitehead, all bore "A" numbers prior to rescue. Along with many other (very well built) MGWR 6-wheelers, they entered departmental service in the late 50s / early 60s and the "A" numbers they now have bear no relation to the originals.
One of the DCDR's stalwarts (an observer of these boards!) has an encyclopaedic knowledge of CIE numbering and can always be relied to to tell us what 486A was, etc.