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I have been trying to think of an adjective to describe a method, an approach, or a way of doing things that covers all of the situations or edge cases. One word that I can think of that is close to the meaning is "versatile " or "well-rounded", or "comprehensive" but I don't think they are the best fit here.

The context is that, I am trying to compare different approaches to achieve a goal and to weigh the pros and cons of each approach. And I wanted to stress that there is one approach that can cover all of the cases. What is the right word that I can use for it?

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You can use all-encompassing

including everything or everyone

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

(M-W)

An all-encompassing approach.

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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]

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  • it sounds weird to me if one says "this is an exhaustive approach/way/method to do something"
    – Joji
    Jan 24 at 19:44
  • 85 000 hits on Google for "exhaustive approach"; I've added one example. 'Edge-cases' surely forces a formal register, while 'exhaustive way' sounds rather incongruous. Jan 24 at 19:50
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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 -

enter image description here

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

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