If research design, data analysis, and results only are good, where is the line between suggesting major revision and rejection?
I would recommend emailing the journal editor to ask for some of these clarifications. There might be certain unwritten policies endemic to that particular journal.
In general, you can ask for multiple rounds of revisions (major or minor) until you are satisfied. Peer review is supposed to be an iterative conversation. However, as I mentioned earlier, there could be certain journal policies regarding the number of revisions which you might get addressed if you talk to the editor.
As a reviewer, if you feel that the article should be rejected, you are free to make that claim. However, personally, I always give at least one chance to a paper (however horrible it is) to redress my comments.