How to approach potential case study companies?
I do not know your field, but I have some suggstions:
1. Define precisely: what is in it for them?
If you are emailing person X in industry to participate in your interviews with some long email like

Dear X,
I am working on [technical research project Y] and I am looking to collect industry opinions on [Z]. I was wondering if you would be interested in helping out with [QRSTUV]...

then probably this email will be ignored or deleted. It is not clear to X why doing this is in their interest. And it sounds difficult for them to learn about your project and figure out how to help.
So I would focus on making your email simple, and explaining clearly why they might be interested.

Is your research likely to benefit the people working in this industry? Say so right up front and explain it from their perspective, not yours.

Is your research in a topic that many people in this industry share an interest in? Pitch this as an opportunity for them to share their expertise and knowledge.


There are many other possibilities depending on what research you are looking to do.
2. Do an internship with the industry
I do not know if this is an option, but in general it might be the only effective way to develop a collaboration. Once you have done an internship, many routes would be open, including collaborating with the industry as part of your research (depending on the field).
3. Get someone more senior (your advisor or someone with connections) to contact them
The industry people will always pay more attention to someone who has status and the possibility of real collaboration and funding that might benefit the industry's interests.