At a glance
～こそすれ means "one may do X (if anything), but definitely not Y". It strongly denies Y by pointing to X, which is usually the opposite or the real situation. It is formal and mostly written.
Verb (masu-stem) + こそすれ、[negative clause]
Noun (of a する-verb) + こそすれ、[negative clause]
この町の人口は減りこそすれ、増えることはないだろう。 This town's population may shrink, but it will probably never grow.
How to form it
| Attaches to | Form | Example |
|---|---|---|
| う-verb | masu-stem + こそすれ | 言う → 言いこそすれ |
| る-verb | masu-stem + こそすれ | 増える → 増えこそすれ |
| する-verb (noun + する) | noun + こそすれ | 感謝する → 感謝こそすれ |
| Passive / causative | masu-stem + こそすれ | 感謝される → 感謝されこそすれ |
| Second clause | usually negative | ～ない, ～ことはない, ～はずがない |
すれ is the classical realis form (已然形) of する, required after こそ (kakari-musubi). It is not the conditional form すれば.
Register: formal, mostly written language and speeches.