I'm sure you could find various examples in the applied SEM literature where individuals have claimed that RMSEA = .09 is "sufficient" in light of other, "better-looking" fit indices but I think that this approach is generally ill-advised. "Approximate" fit indices are problematic altogether, as has been discussed in great detail on the SEMNET listserv (https://listserv.ua.edu/cgi-bin/wa?REPORT=SEMNET&z=4&L=SEMNET&1=SEMNET&X=&Y=). See also the following article:

Marsh, H. W., Hau, K. T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler's (1999) findings. Structural Equation Modeling, 11(3), 320-341.

I would recommend going with the chi-square test and looking at the standardized residual covariances of the model to learn more about why the model does not fit. See, e.g., my Youtube video below:

https://youtu.be/13Xm07Jf5aA

Also, adding multiple correlated errors post hoc (i.e., based on misfit) is usually not a good idea. You may be capitalizing on chance. The subsequent fit indices cannot be trusted because they are based on data-driven model modifications. I discuss this in my following Youtube video:

https://youtu.be/qQhmIMFFOns

Thank you, Christian Geiser ! I will watch the video!

I wonder why you call a value of .09 for RAMEA low; it is advised to be lower. Look at the standardized residuals; maybe one of the items should be discarded. Also, look into the reliability analysis; the same item may pull the reliability down, and look at the factor loading of that same item if it's low that item may be discarded leading to an acceptable value for RAMSEA..

Fadia Nasser-Abu Alhija Thank you for the suggestions! I did not pay attention to low or high. The right is of course lower.