I'd set it in say, 10-15 years after the first one.

Mankind is still dealing with the fallout. New cities are bing built near where the old ones were, or even on top of the reclaimed ruins. New towns are also built, as people get very nervious living in such large groups now.

There are still aliens, mainly survivors from the ships or fighters, who basically hide out and lash out when necessary in a sort of guerrilla existence. Huge bounties are placed on recovering them alive, or dead. Governments fear them trying to send out signals to the rest of their people, if there are any.

Scientists have also spent the last 15 years trying to reverse engineer the now active alien technology. Some new forms of power generation and propulsion are already up and running, leading to new military and NASA space craft / aircraft. Work on the alien weapons and shields is slow though, as the surviving aliens are no help and the technology is so different from our own.

World power structure has changed due to the massive loss of life and military infrastructure. A UN/NATO like organization is now in charge of defense against future alien attacks, as well as maintaining the peace in many parts of the world.

Organizations like SETI, once laughed at, now have massive funding, with the goal or detecting and warning about future alien threats, usual what we know of the aliens communication technology.

after about 15-20 minues of setup, the main arc starts when SETI detects what it believes are several new alien signals, each subtlety different. One set matches the comm signals used by the invaders, while others appear to be different. Officials believe one might be the remains of the defeated race, perhaps their civilian population who normally would have followed the military invasion.

The others they believe may be additional races trying to contact us or inquire about the situation, but humanity is having difficulty understanding the signals without knowing the basis for the alien languages or communication technology.

they do calculate the distance to the signal, and find out it's coming from just outside the termination shock. At current speeds, the first signal, believed to be another mother ship, will arrive in less then 5 months. the other signal is also near, about 1/4th a light year and closing, but won't arrive before the other.

humanity shifts into defense mode, and really starts to gear up for another assault. huge sections of the population are drafted into militia, including Wil's son, now a grown man. aircraft production, and all sorts of weapons increase production, and scientists race to finish work on alien weapons and shields, as well as countermeasures. It seems all these years worth of research and preparation are going to come into use.

In the final arc, before the ship arrives, the surviving aliens launch an all out guerrilla war, hoping to knock out some defenses or soften areas. Not expecting this, some areas are overrun, and humanity races to dislodge the aliens and retatke those areas.

Alas, there just isn't enough time. When the ship arrives, it immediately dispatches invasion ships like those we saw at the end of the first movie. Human defense sats, hastily constructed after the first war, do lots of damage, but are unable to destroy all the ships, and many get though. SAM's and AA guns tear into them as they fly though the atmosphere, again exacting a heavy toll.

some make it down though, and now humanity faces a ground war against an alien foe.

Movie ends around there, When SETI finally manages to understand the other alien comm signal, and realizes it translates to something roughly as 'Endure. You are not alone'.

First sequel ends with humanity in a massive ground war, and awaiting, what we hope, is alien reinforcements.