Looking at a map, the biggest areas of "fragmentation" (lots of smaller nations bunched together) is Latin America, the Middle East, and Africa.
I'm not so sure about Africa, but not having every city/captaincy try and gain independence for themselves in Central and Spanish South America definitely hampered the region. So maybe have the Viceroyalty of Peru not dissolve, or just have the Spanish Empire survive, you could have 2-4 countries instead of the dozen or so of OTL.
You could even get a larger Republic; say the Peru-Bolivia Confederation survives and expands. Mexico holding onto to Central America would also help with this.
For the Middle East, I know it's cliche but having the Ottomans survive would do the trick.