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The phrase "a continuum of increasing" is correct and usable in written English.
It can be used to describe a gradual progression or development in a particular context, often relating to levels, intensity, or quantity.
Example: "The study revealed a continuum of increasing complexity in the participants' responses as they progressed through the tasks."
Alternatives: "a gradual increase in" or "a spectrum of growth in".
Exact(19)
The revised Bloom's taxonomy of educational objectives (Anderson & Krathwohl, 2001) includes six verbs representing a continuum of increasing cognitive complexity: remember, understand, apply, analyse, evaluate and create.
Vasquez et al. (2013) described STEM curricula on a continuum of increasing levels of integration from multidisciplinary to interdisciplinary to transdisciplinary.
A more comprehensive perspective on STEM integration is featured in Vasquez et al.'s work (2013; Table 1), where different forms of boundary crossing are displayed along a continuum of increasing levels of integration, with progression along the continuum involving greater interconnection and interdependence among the disciplines.
As a continuum of increasing clinical severity, severe sepsis is defined as sepsis associated with one or more acute organ dysfunctions [1].
These alternatives can be viewed as existing along a continuum of increasing scalability (see Fig. 1).
The model integrates a continuum of increasing levels of complexity for understanding the impact on QoL.
Similar(41)
Rather, there appears to be a continuum of increased microvascular and macrovasular risk that extends to levels of glycaemia well below these cutoffs.
He theorized that schizotaxic individuals will manifest schizotypy on a dynamic continuum of increasing severity, which ranges from relative psychological health to full-blown schizophrenia, passing through subclinical degrees of deviance and overt personality disorders.
Although increasing age is accompanied by an increased risk of poor outcomes, there is no single cut-off for age but rather a continuum of gradually increasing risk [11 13].
4 In fact, psychosexual and biological factors (including muscular, endocrine, immune, neurological, vascular and iatrogenic factors) that predispose to, precipitate and perpetuate the condition may interact with different degrees in the individual woman, contributing to a continuum of symptoms of increasing severity, with the potential to impair sexual intercourse.
Tangentially related to this, others have proposed that learners who are further along on the continuum of increasing self-determination will be more likely to use L2 learning strategies more frequently and in better combinations, and more willing to invest the time and effort required for self-regulatory learning (MacIntyre and Noels 1996; Noels 2009)—a finding confirmed in our results.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com