My one piece of advice if you are working with 3 or more carseats is you MUST have middle row captains chairs. This way older children can walk back to their seats without anyone needing to flip or slide other seats forward and out of the way for them.
We recently did our car shopping so I am pretty familiar with what is out there for families with 3 or more kids.
What is your budget? I will give you a brief list of what we looked at and what I like and didn't like. All these are current model year that I am referencing.
Toyota Sequoia~ Pros-very comfortable, nice powerful engine, great financing offers, tight turning radius, loved the looks outside. Cons- cheap plastic dash, the model we wanted, the Platinum, has a center console between the captains seats which makes walking to the back seats impossible. I did research and it can be removed but then you have to hide the seat heater wires. Bad gas mileage. Didn't offer black as an interior option. Very little cargo room with third row up and in use.
Ford Expedition EL Limited- Pros-inexpensive for what it offered in comparison to the competition. Loved that the power deploying running boards are standard on the Limited. Very comfortable front seats. Cons- its a Ford which I have never been a big fan of. Captains seats were very ugly and thin as they fold flat onto the ground. Hated the navigation system and the way the rear entertainment system looked.
GMC Yukon XL Denali (basically the same as Suburban, Escalade ESV)- This is what we ended up getting and we have been very happy with our decision. Pros- Great seating flexibility with captains seats which power flip forward if you do need to reach to the third row with the push of a button. I like this because I can flip them forward and sit behind them and reach my kids in the third row to help them buckle or whatever without having to throw my back out or actually climb in the car. Acceleration is there when you need it without the gas mileage being too horrid. I just overall liked this car the best...the looks outside, the interior layout and space, the drive and all bells and whistles.