Historical comparisons are never precise and never exact. They are, at best, suggestive. This does not make them irrelevant or useless, however.

A democratic republic that presides over an empire is not likely to last as a democracy or a republic for very long (Venice, in case anyone raises it, was not a democracy, but incredibly exclusionary and limited oligarchy). Empire usually demands a commitment to militarism and extended overseas adventures; it tends to concentrate power and wealth in the hands of the ruling classes who can benefit most from the imperial arrangements; it is very expensive and can have massive economic effects, unless the provinces are squeezed for cash; and all of these factors will eventually undermine a genuinely democratic constitution. This happened at Athens, in England (where empire led to absolutist monarchy allied to aristocracy), and it may well be in progress now in the USA. There are certainly some worrying signs ...