What is a word that can describe something that covers all of the situations or edge cases

You can use all-encompassing

including everything or everyone

• We're unlikely to find an all-encompassing solution.

(M-W)

An all-encompassing approach.

Exhaustive is a possibility here.

exhaustive [adjective]

examining, including, or considering all elements or aspects; fully comprehensive.

• After exhaustive testing they found that a long track in the circuit board had functioned as the antenna.
• It also explores in exhaustive detail the way Wilson was out maneuvered at Versailles and how he left a broken man.
• The results of an exhaustive study into masculinity were published this week and they make for illuminating reading.

[Lexico]

• Although epicardial intraoperative echocardiography is intended for few patients, it is part of an exhaustive approach to intraoperative echocardiography.

[Journal of Cardiothoracic and Vascular Anesthesia; LudwigGuru]

• A new exhaustive method and strategy for finding motifs in ChIP-enriched regions

[National Library of Medicine]

Generally, I would use comprehensive here. A comprehensive approach to something basically means an all-inclusive approach. But I suppose one may want to make a distinction between a method that includes everything that bears on a single case, and one that is broadly applicable over a domain of cases.

The best bet is probably umbrella model.

It comes with the dubious blessing of a PR firm -

Now, with the Umbrella Model of Public Relations, we have a way to solve those challenges. The model (developed by Game Changer Communications president Jason Sprenger) visually represents the entire spectrum of how people and organizations communicate with their stakeholders and build, maintain and grow relationships with them.

This depiction helps people less familiar with PR understand what it is and how it can deliver value. It also serves as a roadmap to help professionals explore what kinds of communications activities and elements could add value as part of a holistic PR program.

And they aren't about to leave anything to the imagination, either -

https://gamechangercommunications.com/umbrella-model/

The word for this is all-embracing

Applying to or including everything:

an all-embracing definition of art.

[American Heritage Dictionary]