Ten months ago, we submitted an article to a journal, which is still under review. In the meantime, we have made a few extensions/improvements to the submitted article. Can we submit the extended version to another journal? How can we cite the work presented in the article under review? Do we need to inform the editors of both journals regarding the submission of the extended version?
The main issue here is whether the so-called extensions or improvements are substantial enough to classify the revised version as a separate paper. In general, I think not. In addition, that you've "improved" a paper means that the older version is "deficient" in some way (or else, why "improve" it?). If so, then you are doing the original journal a disservice by having them review a deficient paper.
I am part of the editorial team of a number of journals. In none of them would we appreciate you submitting essentially the same paper to another journal. In fact, if we found out, then we would contact the new journal and discuss the case in tandem. In addition, if we received a submission, we expect you to assert that the manuscript was not being reviewed elsewhere. It i likely that you would not be able to make this assertion to us, knowing that an earlier version of the paper was being reviewed elsewhere.
Perhaps you're thinking, "why not submit the revised paper to the same journal because it has improved on the original manuscript?" Even this is pretty frustrating from an editor's point of view. It is likely that, as editor, I'm waiting for reviews of your original paper to arrive. If you were to submit a revision to me during this process, it would be rather disruptive and I would ask why you submitted a half-baked manuscript to us in the first place.
What can I advise you? I suggest that you contact the Journal and ask for the deputy editor who's handling your manuscript. I would discuss your situation citing these two significant issues: (1) 10 months is a long time to wait and (2) during that time, we've made improvements to the manuscript. Then I would ask them what to do.
Deputy editors are human, too. If they understand your situation, then they can advise you accordingly.
In my research area, journals have clearly defined rules that are relevant for this situation. For instance, one particular journal, Software and Systems Modeling (SoSyM), has the following rules:
SoSyM Policy Statement on Plagiarism: Papers submitted to SoSyM must not be simultaneously submitted as is, in an extended form, or in a shortened form to other journals or conferences. Authors can submit extended forms of papers that have previously appeared in conference proceedings. Such submissions must clearly state that the paper has been published elsewhere, must reference the paper in the submission, and must clearly state how the paper significantly extends the published version.
No Self-Plagiarism. Manuscripts in which at least 75% of the content appears in a non-journal publication or in which at least 40% appears in a journal publication will not be published.
You should check the submission policies of your target journals carefully for such rules.
As noted by others, there may be a problem if the extended paper isn't original enough to be a separate publication.
Another problem is: what about potential requests for revision when you get feedback from reviewers on the original paper?. They might ask for some of the very improvements you have already made. Or they might ask for changes that put this paper out of line with the "extended" version. In either case, you have a bit of a mess if the extended paper was already submitted elsewhere.
In any case, I think you need to wait until you have a decision on the first paper to proceed.