In my medieval world, a union of five states located on the south shores of a continent much like Europe is a subject of joined invasion by a northern continental empire and marine power coming from a distant southern continent.
The five states are well-developed countries with big cities, strong army and navy, good roads and many navigable rivers. They are all located around the coast of an inner sea roughly the size of the Black Sea and the land area of the states is comparable with the size of the countries on the Balkans or Central Europe (Bulgaria, Greece, Serbia, Hungary, Czech Republic and etc) or Ireland if you're not familiar with the geography of Central and Eastern Europe. The inner sea is connected with the ocean by a narrow strait filled with small and medium-sized islands (like the Greek islands). The borders of the five states are well defined by long mountain ranges and rivers but there are also some rivers and mountains which crosses the borders and splits some of the states into different provinces just like the way Balkan mountains splits Bulgaria and Danube river splits Hungary. All five states have their own rulers but in case of war or another emergency the states respond as a single entity and combine their armies and resources to handle the threat. The five states have central governments and are ruled in the manner of ancient Rome, with fair taxes and laws, local governors, public spendings etc. Generally, the people are happy with their rulers and the quality of life is better compared to neighboring countries.
I'm trying to figure out a scenario in which the invading army manages to seize control over most of the strongholds around the river banks and the seashore and by doing so preventing the five states to communicate and organize and forcing them to fight separated. Controlling the mountain passes is also a requirement but it can be achieved later in the war.
The northern continental empire
Some of the border rivers spring from the mountains in the north, deep into the territory of the invading northern country. Maybe they'll use their river fleet to quickly move troops south and besiege the cities near the banks. Of course, there are river chains that protect the border but the invaders may find a way to bypass it (it will be nice if you find quick a way of doing so). After reaching the city walls either with ships or on foot after landing the attackers will use some new technology provided by their foreign ally to attack the walls or maybe they will use the element of surprise. Is it possible to take control over ten to twenty fortified cities in just a few days (as few as possible) and what technology or tactics can be used?
The southern marine empire
The second invading force will use its mighty fleet to raid the coastal cities around the inner sea. The first obstacle is the heavily guarded strait with three main strongholds called Eyes. The East Eye and the West Eye are located on the edges of peninsulas and there are trading cities with the same name nearby while the Middle Eye is placed on an island in the middle of the strait and it is just a military base without a major settlement nearby. Each of the eyes is managed by different state (food, salaries, repairments etc.) but the commander of the Middle Eye is the one in charge who commands the troops. The three fortresses act as naval bases and guard the passes around the islands. Their main purpose is to prevent pirates from entering the inner sea and plundering the trade roads but the number of ships stationed there is big enough to repel an invading fleet. I'm thinking about a surprise attack on the harbors while all the ships or at least a large number of them are inside. The defenders will be unable to react and the Eyes will be captured. Maybe during the night most of the ships are in the harbors or there is a storm approaching or there was a storm already and the ships needed repairing. I'll be glad if you find a solution. Is any of these a possible scenario? Another option is to ambush the ships somehow and sink them in a naval battle.
Then after securing the strait the invaders will enter the inner sea and attack the largest ports. These ports are also guarded by fleets but relatively small in size because the defense of the strait is considered impregnable. The foreigners don't have to hurry and it will be enough to perform a naval blockade. Of course, they will prioritize taking some of the cities because they will use the ports as bases to deploy the army and proceed inland but for most of the cities, there is no need to attempt breaching the walls. It will be even better if there is a way to burn the defending ships while still in the harbor or at least to drive them into a single naval battle to destroy them all at once. If there are no ships to transport troops from one place to another it doesn't matter who controls the coastal cities.
The technology level is similar to that of Late Antiquity and Early Middle Ages. The Southern empire may have some advanced technologies but not something too advanced. Better navigation, stronger ships or even some kind of explosives but weak and used on rare occasions are all fine. It should not be something the defenders can't understand and replicate over time.
So, let's summarize. A confederation of five states is invaded by two empires. The first goal is to cut off the states and prevent them from helping each other. How could this be achieved?
If more details are required I'll provide them with comments.