You are correct that 佐藤さん is the topic in these sentences, but your understanding that も can be used "when the topic remains the same" is incorrect.
The actual usage of も is the opposite - it introduces a new topic (or other element in the sentence) to which the same statement applies. The word to which も is attached should be the only element in the statement that does change, not the only element that doesn't.
So the following pair of sentences would make sense:
佐藤さんは会社員です。 (Mr Sato is a businessman.)
田中さんも会社員です。 (Mr Tanaka is also a businessman.)
But the pair you suggested makes no sense, because も is attached to the same thing in both sentences.
The confusion may arise because the English word "also" actually acts on the entire sentence rather than any specific word, and so can function identically regardless of which element has changed. For instance:
Mr Sato is a businessman.
Mr Sato is also a Japanese person.
In English, this makes sense and has the exact same structure as the above pair, even though this time it's the latter element that has changed. In Japanese, however, the structure of this pair would be different - you would need to attach も to the latter element:
佐藤さんは会社員です。
（佐藤さんは）日本人でもあります。
In these examples, the topic (佐藤さん) remains the same, so it can and usually would be omitted in the second sentence. も in this case is not attached to the topic, but to the predicate 日本人です (which has to be expanded into the fuller form 日本人であります when も is used).
In a sentence with an ordinary verb rather than です, the usage of も is a little more straightforward - it simply replaces は if the topic changes, が if the subject changes, or を if the object changes. So:
佐藤さんはワインを飲みます。 (Mr Sato drinks wine.)
田中さんもワインを飲みます。 (Mr Tanaka also drinks wine.)
佐藤さんはワインを飲みます。 (Mr Sato drinks wine.)
佐藤さんはビールも飲みます。 (Mr Sato also drinks beer.)
佐藤さんが来ました。 (Mr Sato arrived.)
田中さんも来ました。 (Mr Tanaka also arrived.)
