Two sentences point the same way when they support the same conclusion. “Remote work removes the commute” and “it lets people live further from expensive centres” are both arguments for remote work, so an addition connector is honest between them. The test is not whether the sentences are about the same topic — they usually are either way — but whether a reader who agreed with the first would be moved further along by the second.
This is why the commonest error with this family is not a misspelling or a comma. It is using “furthermore” to join a benefit and a drawback. The reader has been told to expect more of the same and receives the opposite, and the paragraph reads as though the writer lost track of their own argument halfway through — which, from the reader’s side, is exactly what happened.
The second thing worth knowing is that these connectors do not all behave alike grammatically. “Furthermore” opens a sentence and cannot take an object; “in addition to” takes a noun and cannot open a clause on its own. Two words that mean the same thing, two different structures, and swapping them produces a fragment.
Both sentences support the same conclusion. If the second qualifies the first, you need contrast instead.
“Moreover” suggests the new point settles the matter. Use it for your strongest addition, not your third.
“Furthermore, X happened” takes a clause. “In addition to X” takes a noun. They are not interchangeable.
“Not only does it cost more…” — the verb moves in front of the subject, and forgetting it is the classic slip.
