Any hand in a storm.
(Neko no te mo karitai; “Wanting to borrow even a cat’s hand”)
Being so extremely busy that one is willing to accept help from anyone at all. So busy that any helping hand is welcome, regardless of whose it is – even if the one lending a hand is a mere cat. Cats were apparently thought to be useless aside from keeping vermin in check, but sometimes even a near-useless helper is better than none at all.
This saying is technically a full sentence, although an explicit copula would make it more of one. The primary noun is 手 (te), “hand,” marked by the associative particle の (no) as belonging to a 猫 (neko), “cat.” The particle marking the whole noun phrase is も (mo), commonly translated as “also” but in this case closer to “even.” And we end with the verb 借りる (kariru), “to borrow,” in conjunctive form with the suffix たい (tai), which expresses a desire to perform the associated verb.
(“Tsugi kara tsugi e to kyaku no chuumon ga haitte kite, Kyouko-san wa ureshikatta ga, tsui ni isogashisa no amari ni, neko no te mo karitaku naru kibun wo oboeta.”)
[“With orders coming in one after another Kyouko was happy, but in the end things got so busy that she found herself feeling that she wanted any help she could get.”]