Here is the challenge, applied to several countries:
Rome survives as a Republic at least100 years longer than OTL
Britain remains a non-monarchical Commonwealth for at least 100 years after the English Civil War
France remains a Republic without monarchical interruptions for at least 1792-1892
Netherlands remains a Republic through late 18th and 19th century at least
Venice remains a Republic through the 19th century
Naples remains a Republic for at least 1647-1747
Modern Greece remains a Republic for at least 1822-1922
Spain remains a Republic at least 1873-1973
Lanfang remains an independent Republic at least 1884-1984
Hungary remains a Republic at least 1848-1948
Japan remains a Shogunate, or turns into a Republic, without Imperial power, from at least 1868-1968
Brazil becomes independent as a Republic, never a monarchy
Mexico becomes independent as a Republic, never a monarchy
Rome survives as a Republic at least100 years longer than OTL
Britain remains a non-monarchical Commonwealth for at least 100 years after the English Civil War
France remains a Republic without monarchical interruptions for at least 1792-1892
Netherlands remains a Republic through late 18th and 19th century at least
Venice remains a Republic through the 19th century
Naples remains a Republic for at least 1647-1747
Modern Greece remains a Republic for at least 1822-1922
Spain remains a Republic at least 1873-1973
Lanfang remains an independent Republic at least 1884-1984
Hungary remains a Republic at least 1848-1948
Japan remains a Shogunate, or turns into a Republic, without Imperial power, from at least 1868-1968
Brazil becomes independent as a Republic, never a monarchy
Mexico becomes independent as a Republic, never a monarchy