One obvious starting place to investigate a possible violation is to fit the separate logistic regression models, and inspect which odds ratio(s) are heterogenous.

glm(I(y>1) ~ x, family=binomial)
glm(I(y>2) ~ x, family=binomial, subset = y>1)
glm(I(y>3) ~ x, family=binomial, subset = y>2)
...

When the proportional odds assumption holds, we expect the coefficient of x to be the same in each model. A lot of times, "intermediate" quantities tend to be pretty sparse, especially for questionnaire data. In those cases, you may find odds ratios that are wildly variable, and it's enough to miscalibrate any sort of global test like Brant. The solution at times may just be to dichotomize data, since such an analysis while potentially inefficient, would be well understood and generalizable - or alternately, you might simply fit a simple linear regression model! Treating ordinal outcomes as continuous is widely discussed, widely accepted, and highly generalizable, even in spite of the issue of "overprediction".

One obvious starting place to investigate a possible violation is to fit the separate logistic regression models, and inspect which odds ratio(s) are heterogeneous.

glm(I(y>1) ~ x, family=binomial)
glm(I(y>2) ~ x, family=binomial, subset = y>1)
glm(I(y>3) ~ x, family=binomial, subset = y>2)
...

When the proportional odds assumption holds, we expect the coefficient of x to be the same in each model. A lot of times, "intermediate" quantities tend to be pretty sparse, especially for questionnaire data. In those cases, you may find odds ratios that are wildly variable, and it's enough to miscalibrate any sort of global test like Brant. The solution at times may just be to dichotomize data, since such an analysis while potentially inefficient, would be well understood and generalizable - or alternately, you might simply fit a simple linear regression model! Treating ordinal outcomes as continuous is widely discussed, widely accepted, and highly generalizable, even in spite of the issue of "overprediction".