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あの会社と

with that company

→ あの
phrase Rare #35,776
with that company と marks the company as the other party in an action or relationship. Before a following noun, it becomes との.
JA: あの会社と新しいプロジェクトを始めました。
EN: We started a new project with that company.

我が社はあの会社と取り引きをしている。

Our company does business with that company.

あの会社との契約はあってなきに等しいものです。

Our contract with that company is practically meaningless.

わが社はあの会社と契約を結んだ。

Our company signed a contract with that company.

我々はあの会社と激しく競争している。

We are in fierce competition with that company.

彼女はあの会社と取引関係があります。

She has a business relationship with that company.