Dealing with legacy systems: when to rewrite vs incrementally improve

we're facing a classic dilemma with a 10-year-old php monolith: no tests, outdated dependencies, and a general fear of touching anything. management is keen on a full rewrite to go, hoping to modernize and accelerate. but the team is wary, having seen failed rewrites before. i need a framework for making this rewrite vs. incremental improvement decision. what are the key factors to consider? how do you quantify technical debt against the risk of a full rewrite? when is it genuinely better to bite the bullet and rewrite, and when should we focus on strangling the monolith or gradually refactoring it module by module? i'm looking for practical, experience-based criteria.