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'There is no way one could X' — the action is impossible from the outset, given one's position or circumstances. Literary; used with verbs like 知る, 望む, 比べる.
V-dict + べくもない；する→すべくもない
〜べくもない
Double negative meaning 'it's not that I don't…' — grudging or partial admission. Neutral spoken and written; softens the speaker's stance.
V-nai stem + なくもない；i-adj く + なくもない；N・na-adj で + なくもない
〜なくもない
Double negative 'not entirely un-…': the speaker admits a slight degree of feeling or willingness, with reservation. Slightly formal.
V-nai + でもない（〜ないこともない と同義）
〜ないでもない
'As if about to do X' — describes an appearance or manner that stops just short of the action. Literary; used to describe others.
V-nai stem + んばかりに／んばかりの + N；する→せんばかり
〜んばかりに
'Even if you do X, it won't help' — a hypothetical whose result is useless or negative. Always followed by a negative or futile outcome; slightly formal.
V-ta + ところで（後件は否定・無意味な結果）
〜たところで
'Nothing beats X / it's best if X' — states a commonsense preference, often as friendly advice. Common in both speech and writing.
V-dict／V-nai／i-adj／na-adj（な・である）／N + に越したことはない
〜に越したことはない
Formal 'by means of' (method) or 'as of' (a set time at which something takes effect or ends). Typical of notices and ceremonies.
N（手段・時）+ をもって
〜をもって
'On the basis of / taking X into account', where X is data, opinions or past experience used as a foundation for a decision. Business and academic register.
N + を踏まえて／を踏まえた + N
〜を踏まえて
'You can't get away without doing X' — social pressure or circumstances make the action unavoidable. Formal written equivalent of 〜ないでは済まない.
V-nai stem + ずには済まない；する→せずには済まない
〜ずには済まない
〜べく Formal, written 'in order to'. Same as ために but restricted to reports, news and stiff speech; the following clause states a deliberate action. — V-dict + べく；する→すべく（するべく）
〜をよそに 'Paying no attention to X', where X is others' worry, opposition or expectation. Critical or detached tone; written register. — N（他者の感情・反応）+ をよそに
〜に堪える 'Is worth doing / can bear' — the thing has enough quality to be worth reading, watching or appreciating. Formal written; the negative 〜に堪えない is more common. — V-dict／N（鑑賞・使用など）+ に堪える；否定は 〜に堪えない
〜を禁じ得ない 'I cannot help feeling…' — a spontaneous emotion the speaker cannot hold back. Stiff written register; only with emotion nouns. — N（感情を表す語）+ を禁じ得ない
〜を機に 'Taking X as an opportunity', where X is a turning point that prompts a positive change or new start. Slightly formal. — N + を機に（して）／を機として
〜をものともせずに 'Undaunted by X' — someone faces a hardship or obstacle without letting it stop them. Written, admiring tone; not used about oneself. — N（困難・障害）+ をものともせず（に）
〜を余儀なくされる 'Be forced to do X' by circumstances beyond one's control, with a sense of regret. Formal written and news register. — N（動作性の名詞）+ を余儀なくされる
〜を境に Marks a point in time as a dividing line: before and after it, the situation clearly changes. Neutral-to-formal, often written. — N（時・出来事）+ を境に（して）
〜手前 'Since I'm in front of / have said X, I can't back out' — social face obliges the speaker to act a certain way. Spoken and written, slightly formal. — N の + 手前；V-dict／V-ta／V-ている + 手前