Countermarks are fascinating but even more so when they are applied over one another.
The researcher is left to ask when, why and how.
This blog post has attempted some answers based on an unusual mark and it is hoped that others will supply more ideas for further research and study.
Cromford Derbyshire Countermarks – by Eric Hodge
BNS Research Blog 
A very interesting observation and it is very clear that the lettering on the 5/- is different to the 4/9, but this is not surprising as these two punches would have been made at different times, however, the original style was followed quite closely.
What intrigues me is ‘why’ go to the effort of erasing the 4/9 value in order to then stamp the coin for 5/- when we can see that other 4/9 examples were simply ‘overstamped’ 5/-. I wonder if seeing the remnants of the 4/9 under the 5/- overstamp might have created adverse feelings among the recipients of these coins in that it would appear that the company was simply making an extra 3d profit by ‘reissuing’ the coins?
I don’t really understand the actual ‘process’ of erasing the value, but leaving the rest of the letters intact. It strikes me that this would not be an easy or efficient process. Would it not be easier to erase the entire countermark rather than just the central part of it.
A closing thought: Could someone with a 4/9 coin think that if they could erase the value they might be able to install, in some manner, the higher 5/- value and enjoy the 3d profit themselves?
Ken puts forward an excellent idea of a possible fraudulent intent for a 5s punch. I have 15 photos available for study of the 5s mark and all have the 5s lettering, so none have retained the 4/9 lettering with a 5s mark.
This leads on to an analysis of the 5s marks for future reference.
7 show only the 5s value and wording, with no previous marks visible, though some do appear to show a previous strike or double strike.
5 show all or part of 4/9 under the 5s but no previous lettering.
2 show the 4/9 and some previous lettering.
1 shows some of the previous lettering, but none of the 4/9 value (Fig. 3).
It is Fig. 3 that perhaps indicates it was possible to over-strike and erase the 4/9 value.
As the value was the most important aspect of the countermark, it was important to ensure as little as possible of the 4/9 remained in the new strike. The name round the value was the same (though different lettering) but was basically cosmetic. If work was needed to be done on the 4/9 mark before re-striking, then only having to erase the value created less work and perhaps Fig. 4 was the start of this process?