Q: Can I submit a modified version of an already submitted paper to a new journal?

Is there any special reason why you wish to do that? If the purpose is to increase the number of your publications, then it is highly unethical and would be considered a case of self-plagiarism and/or duplicate submission. 

However, if you are using a new method to address the same research question from a different angle, it should be possible to write a paper on this. Of course, you have to cite the previous paper and clearly state in the abstract and cover letter that this paper is based on the previous work. However, ideally, you should wait till the first paper is published before submitting the second. Else, it might seem like the case of a duplicate submission.

However, remember that the manuscript of the second paper should be completely different; everything, including the literature review, discussion, and how the results are presented, should be distinctly different from the previous paper. If the two papers are not clearly different in focus and presentation, then they might be considered as duplicate submissions. Therefore, you should be very careful about this. 

If you feel that the two papers are very similar or have a lot of overlapping content, then you can consider publishing the second paper as a “Methods” article where you describe only the methodology used in great detail. Many journals publish Methods articles. For instance Nature Methods is a journal dedicated entirely to “the publication of novel methods and significant improvements to tried-and-tested basic research techniques.” Alternatively, the second paper can be a follow-up study of the first paper in which you clearly state at the beginning that you have used a different method to address the same research question that you had used in a previously published paper.

Whichever option you choose, you should be transparent and disclose everything. You should mention your published paper in the cover letter and abstract, and cite the published paper wherever you are using material from it. You should ideally attach a copy of the published paper and send it to the editor along with your manuscript.

You might also be interested in knowing if it is possible to publish two papers using the same data and methods but a different focus.