You can submit a paper "sufficiently" different from the journal paper, which it sounds like you are doing. (Sufficiently different is a judgement call.)
Note, however, that one of the main criteria for acceptance at most reputable journals is "novelty" of the ideas and conclusions. If you "step on" that novelty in a new paper, then it might cause issues.
Some will wonder if you are "salami slicing" to get two publications out of one idea, but if, for any reason, what you do in the second paper wouldn't have been appropriate in the first then you should be ok.
And, of course, the second paper may not have the necessary novelty for acceptance.
Make sure you properly cite the first paper, of course. In the short term, mark the citation as "under review". You may need to update that before final versions are submitted.