Consider
(…) and they were getting stronger with/for every day
What's the difference/the correct one to use?
Learn English – “For every day” vs. “with every day”
differencesprepositionsword-choice
Related Solutions
Most, as an adverb, can be used informally to mean “almost”. In that sense, there is no difference in meaning between “most every” and “almost every”, except that the first one is informal.
I should add that the Corpus of Contemporary American English has 290 occurrences of “most every”, compared to 5027 for “almost every”. The second alternative is thus vastly favoured, at least in written American English.
In the British National Corpus, “most every” returns 4 occurrences, while “almost every” returns 788 hits. It thus confirms what commenters have said, that “most every” is a regionalism.
"at" every step vs. "on" every step.
In both phrases, both "step" are nouns; but, different nouns.
If "at" is used, the "step" is what a person makes while walking, one step at a time. Therefore, "at every step" a reader is going to imagine a person is actively walking. Also, that something else is occurring in the background during every step that person takes. (Example: "The monster was behind her at every step." [No matter which direction the girl walked, the monster was right there behind her] - It can also be a "step" or procedure like below with "on," so it's important to read what's around this phrase to ensure you're taking it in the right context.
If "on" is used, the "step" is a different noun as another poster pointed out. "On' turns the emphasis away from the person taking action, to emphasis the step as more crucial. "Step" - It could be a physical step on a staircase, or ladder, or, like cited last above, a "step" or a specific procedure one must do or follow in constructing or assembling something.
(Example #1: While climbing the ladder to pick cherries, "Warning: Serious Injury May Occur if extended beyond 5 Meters" was written on every step.) ..that is, each and every ladder step had this warning on it to ensure a person wouldn't extend the ladder beyond what it was safely designed for.
Example #2: "In building any model airplane with high voltage, safety equipment must be worn on every step, when performing steps 8 thru 14 below:" [Whenever steps 8 thru 14 are performed, no matter which step it is between 8 and 14, safety equipment is necessary to prevent serious injury.)
To answer your question, you seem to be translating some kind of 'life lessons" work where steps are metaphoric, like in steps you take in life or decisions you made at specific turning points ("turning points" - metaphor for path or step.) Therefore, apply what I wrote in paragraph 1 (at) if emphasis is on the actions of the person, which this fits best, since at every turning point where action was required, the narrator chose to deliberately protest & object. Apply paragraph 2 (on) if you decide emphasis is better stressed when placed on the step or path (every path - metaphor for any and all good or bad paths a person could take in life) the person has been on all these paths, and no matter which kind it was, just protested 7 objected.
If this is the case, which I think it is, that your translating a metaphor for life's steps taken along the way, either one works; but, the stronger impact is "at" - since life is active and "happens" based on what we as living people do or don't do in our lives that have real impact or effect, so I would choose "at." Why?
The "stressor" in the poem is on the person and their decisions at life's critical points, so use "at." If you as the writer or translator, however, is attempting to stress the "path" like the right path..being on the right path is sure and secure, and a person didn't follow it, or on the "right steps" in a marriage were taken = happy; weren't taken = full of troubles, "on" puts the writer's stressor on the path or the step, so then use "on."
In metaphor, it's up to you as the writer to point me as the reader concisely what you're trying to convey. I Hope this helps.
To apply above to your work:
"At every step, at every path, I've protested/objected"
Me (Reader): I read this and think the 1st person (writer), all along the way in life ("step" "path" = metaphor for "life), this person has constantly protested and complained. (Summation: This person has come to a crossroads in their life where they see they've lived wrong in the past and it's a pinnacle point to awareness as first step to change behavior for the good) Emphasis again is on the actions (metaphor for path or step) the narrator has taken.
"On every step, on every path, I've protested/objected" Me (reader): I read this and think no matter if this person was on a good path or bad one ("every step" "every path" - metaphor for living good life or living a life of crime - as "both" encompass "every path" even down the sexual ones or study ones..no matter the path, it didn't matter. This person complained, protested, and objected whenever doing right or wrong, or anything-everything, nothing mattered and "I've protested/objected" - is a firm statement this person is not going to change no matter what new "path" or step you might propose to them to follow, they're not going to do that, either. Emphasis is on a good life or bad life (encompasses "every" path) and this person still complains either way.
Best Answer
With is correct here because it indicates the "getting stronger" and the "every day" are occurring simultaneously, or with each other. For is incorrect here because it would indicate that whoever/whatever is getting stronger is doing for the purpose of "every day," which is nonsensical.
However, the preposition could be dropped altogether with no loss of meaning: