To ask for THE holy grail vacuum cleaner?

[overweightcat]

Live in a small cottage type mid terrace.
Me DP, 2 under 5yo.

All downstairs is slate flooring which is slightly uneven - so it would have to have REALLY good suction.
All upstairs and staircase carpeted apart from bathroom.

We had a Henry which was fab and really made the (quite old) carpet look great after vacuuming but it's weight and bulk was a real problem when manoeuvring around the house and constantly falling over.

We went for the cordless shark as I loved the idea of just whizzing around the house with it but it's useless on the slightly wonky stairs and picking up bigger pieces of fluff that we tend to accumulate around the house with all the day to day goings on. It needs waaayyy to much maintenance to maintain any suction and it's absolutely useless on the slate tiles too. And do not get me started on attempting to vacuum the car.

So ideally we need something with really strong suction but smaller/lighter than the Henry a few different attachments would be a bonus. Corded is fine.

Any recommendations would be really appreciated as we are at the end of our tether with this one and have made our minds up to get a new one.

I have a Miele but not the cat and dog. Suction is very good. I have 3 heads for it. The regular one, a turbo head and one which is a brush head which is great for wooden floors to avoid scratching them. I actually have one I bought a few years ago before the wattage changed to replace my currentvone when it dies. I think It goes up to 2200 watts. I also have a Dyson cordless which I got on offer in Tesco for those quick clean ups which isn't doing to well atm.