I was recently challenged to consider how I would "turn a 3* into a 4* impact case study". My simple reaction was: you can't. But there are things that you can do, depending on how close to REF submission this question is being asked. The key is to separate "impact" and "case study".
I'm presenting this as 3 steps, but I want to highlight straight away that without the first step, you can forget the other two. And of course, these steps are the same for any kind of research impact heading towards REF. Just delete 4* from each heading as you read - I've included it to emphasise that without 4* impact, you cannot write a 4* impact case study.
Step 1: Create 4* impact
At the time of writing (in 2024), the REF2029 submission is over four years away. There is a lot of impact to be developed between now and then, and in some cases, it is possible to create 4* impact from something that would end up as 3* impact if left alone. You can extend the reach, and potentially the breadth of the significance; you might identify other beneficiaries that might benefit slightly differently from the same change. To increase the chances of this happening, careful and comprehensive planning is essential. I'd start with a broad analysis of everyone who might be relevant to the research: those who are (potentially) impacted, interested, and influential. From there, you can develop action plans, timelines, backup plans. None of this will guarantee you a 4* rating of your case study, but at the very least, you've done what you can(1) for those whose lives you are hoping to improve in some way, with the help of your research - and this is not only more important, but also the best foundation for creating impact that will be highly rated in the end.
Step 2: Evidence 4* impact
The bridge from far-reaching and significant impact to a highly-rated impact case study is being able to evidence said impact. You'll need evidence of the nature of the change (articulating significance is really important here - don't over-focus on reach) and of the link to the research. Again, planning is crucial here: can you get a baseline? Can you collect evidence as you go along, while partnerships are fresh? Can you check in again nearer the time, to see if the scale has changed and whether any additional benefits have arisen? That way, you maximise the ability to claim as much as possible, as convincingly as possible, for assessment purposes.
Step 3: Present 4* impact in a 4* impact case study
And then finally, in 2028, you can write the best case study that your impact allows. By then, there will be a host of advice for presenting case studies (for now, there's my article with Mark Reed and others and the associated blog post). At that point, "turning" a 3* into a 4* is possible if the label "3*" refers to the write-up, not the impact itself - that is, if you're looking at a 3* write-up of 4* impact. Then the task is to do the 4* impact justice by highlighting the best part, presenting that in the best way possible (i.e. obvious, explicit, specific, convincing), evidencing it best, making it a joy to read (depending on topic!) and generally making it impossible for the assessor to mark it down.
So, the more nuanced answer is:
You can take steps to extend 3* impact to 4* impact, if you have the time.
You can ensure that your case study of 4* impact actually describes and evidences that impact in a way that you can get the full credit in the assessment, rather than losing points by accidentally presenting your 4* impact as something more like 3* impact.
But I stand by the assertion that you cannot "turn" a 3* impact case study into a 4* impact case study - to me, this question implies "presenting 3* impact in a way that it gets a 4* rating", which in my value system should not be possible. And no one preparing an impact case study can say with certainty what decisions are made behind closed doors by a team of assessors, so the best thing you can do anyway is to create impact for the sake of the benefit from your research, rather than for the sake of the benefit from research assessment.
(1) Hopefully within working hours, or thereabouts - "done what you can", in my world, does not entail "pursue this until you break".