Carry-on luggage cart to transport 2 suitcases?

You should give more information, like to what country are you moving. If Germany, German Rail has a luggage delivery service. You could leave the suitcases at a location in one of several airports and it would be delivered to an address in Germany.

I left my destination vague because I wanted an answer about luggage carts not services. Let's assume that there are no services.

You mean like this?
https://www.amazon.com/dp/B06XYPGCCS?psc=1

Amazon lists all kinds of foldable luggage carts.

Asking for your destination wasn't an unreasonable question, since we might have been able to offer viable aternatives.

Since most luggage these days has either 2 or 4 wheels it is becoming very rare to see them. I've never seen one for two suitcases, let alone two very heavy ones.

By refusing to help us help you it is impossible to help much. Many of us have plenty of experience of travel in virtually all European (and non-European) countries who could help you find a suitable solution. You could be moving to Switzerland or Somalia or Siberia; Great Britain, Gabon or Georgia.

Better check how you will get these huge heavy suitcases up to the platform, and then up the (how many?) steps onto the train, and where you will be able to store them on the trains, and then the same in reverse, in a short period of time.

moving to Tokyo

I suggest pairing down what you bring, and getting 2 large rolling cases and a good back pack.

I would be surprised if your apartment could hold more than that amount of goods anyway.

I have seen many street vendors, musicians and photographers use this in NYC

https://www.amazon.com/dp/B01G5VGGFA?psc=1

Since the cart in your link appears too big to be a carry-on, can it be strapped onto one of the suitcases and be considered part of the bag?

If you are moving to Japan, you might want to look at their luggage delivery services. We used one when travelling by air within Japan. You can drop off your bags at the airport counter on arrival and they will deliver it to your hotel or residence. Once you've been there a while, you'll notice very few Japanese checking bags or carrying bags onto flights within the country. They use the luggage services instead.

I think you need to define 'very heavy' first and then decide what cart will carry it. What optipns you have depends on where you are moving from. Despite this being a Rick's website, there are global responders. Then decide whether the cost of the cart, possibly an additional cost for both weight and a third bag would be balanced with taxis or a delivery service.
Personally, I would hate to have to move my life in two 40 pound suitcases.....I hope you find a solution.

Lots of us do this kind of move overseas for 6-12 month research sabbaticals or teaching. This is when we have large suitcases, books, computers, but we use porters, taxis, delivery services. It's hard enough to keep the weight under 23kg for a move without adding a cart. One of my kids went overseas to teach but he just wheeled his large suitcase down the streets.

Luggage delivery service in Japan is awesome, efficient, and it's what most people use. The price is very reasonable. It's not like shipping something. You don't have to speak Japanese. Just have your address written down.

A lot of subways and train platforms only have stairs, no elevators or escalators. If you have a heavy suitcase or two it will be really difficult. I lived in Japan a year before I found out about this service.

When I moved to Japan I used an army duffel bag. You could also get the largest Eagle Creek or REI duffel bag. Roll your cloths up very small and stuff the into the duffel. Duffel bags can be rolled up into nothing which will be very useful in Japan.

Japan probably has more of these kind of services than lots of places.

Thanks for all of your replies. They have been very helpful.