I know every classifier in Chinese has its own usage and place. For example 头(tou2) is for domesticated animals, and should not be used for a "refrigerator". What has become a question for me, is, some classifiers have "definitions and uses" which overlap that of the others.
For instance, the classifier for 猫(mao1):cat is 只(zhi1). On the other hand, 头(tou2) is the classifier for domesticated animals. Considering this, is it correct to say 一头猫 instead of 一只猫? How would it sound? Do Chinese classifiers have such flexibility? (In a way that a single noun can fall into different categories of classifiers)
Other examples are: the classifier for 镜子(jing1zi):mirror is 面(mian4):classifier for flat objects On the other hand, 台(tai2) is a classifier for heavy objects. So if a mirror is heavy, is it correct to say 一台镜子
Or, the classifier for 桌子(zhang1zi):table is 张(zhang1):classifier for flat objects. On the other hand we know that both 片(pian4) and 面(mian4) are also classifiers for flat objects. So, how would it sound if we say 一面桌子 or 一片桌子.