〜てでも
even if it means (doing)
Verb て-form + でも
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てでも expresses strong determination: the speaker is willing to do something drastic to achieve a goal. 借金をしてでも、この家を買いたい, "I want to buy this house, even if it means borrowing money".
The first half is a sacrifice or an extreme measure (borrowing, staying up all night, taking time off, queuing). The second is the goal: たい, つもりだ, or a firm statement.
It's the て-form plus でも. With verbs whose て-form ends in で, it becomes ででも: 休んででも, 並んででも.
Compare ても ("even if"), which is neutral. てでも says "I'm prepared to go that far". 何をしてでも means "whatever it takes".
Examples
借金をしてでも、この家を買いたい。
I want to buy this house, even if it means borrowing money.
徹夜してでも、明日までに終わらせる。
I'll finish it by tomorrow, even if I have to stay up all night.
何をしてでも、夢をかなえたい。
I want to make my dream come true, whatever it takes.
仕事を休んででも、子どもの試合を見に行く。
I'll go and watch my child's match, even if it means taking time off work.
並んででも、あの店のラーメンが食べたい。
I want to eat that shop's ramen, even if I have to queue.