This is the first cartridge I have reloaded that required expanding the case neck. The dies I have are equipped with a long tapered expander button but I still can't expand the necks without collapsing the case. I have other dies in 6mm, 257, 264, and 277.
What lube do you use? How many steps does it take? Any other information will surely be welcomed.

Try the Redding Imperial Sizing Die Wax.

Also chamfer the inside of the case necks before you expand them.

Once upon a time I had a Contender in 7mm TCU.

My Pacific Durachrome 7mm TCU dies have a long tapered button too but only .312 of the taper length actually does the work. I'm doing an inventory of my stuff so I found 5 old cases LC 81 5.56 cases that had been fired and resized to .224.
I lubricated them generously with Redding Imperial. Using very slow steady pressure I was able to open up 4 of my worst cases with one pass. Then I found a crushed case and pried it open with a tapered punch. It also expanded to 7mm in one pass and would even have blown out to make a usable case again.

Just experiment with what you have but use plenty of lube or relube part of the way through the expanding process.
Have your cases been annealed. Annealing can make the neck easier to expand but it can also make the shoulder so soft it can collapse. My cases were not annealed.
Expand a few cases in steps to each smaller diameter and then step up to the 7mm expander.
You may have to ruin a few cases but you will know how many steps it takes.

I used to have 50 or 60 7mm TCU cases somewhere.
If I can find them you are welcome to them.

RCBS lube on a nylon brush. Run the case into the die part way, back out. Do this about 3 times. In other words, don't size all in one stroke of the lever. Some FL dies should not contact the shell holder for correct head to datum adjustment.

Any kind of decent lube INSIDE of the neck.

It should "shoot out" in the fire forming loads and give normal friction/neck tension after that.

Just had this same issue resizing my first 223 brass to 7mm TCU - had to adjust my sizing die to where I was not sizing the case at all, just expanding the neck. Then fireformed brass, then ready to re adjust the die and resize as with other cartridges.

I fould I was expanding the necks at the same time I was resizing, so really shoving the necks down into the brass.

Guys over on specialty pistols helped me figure it out.

Thanks all, I picked up some Imperial wax, cleaned the cases and inside necks well, then decided to try and neck them up to 6mm to start. I'll polish the expander in the TCU set of dies and finish sizing to 7mm later today. The 6mm sizing went well.

Is brass that different now?
Back in the '80s, I simply lubed the 5.56 cases as usual to resize and ran it through the sizing die. Did about 500 and don't remember losing even one case. Used wax bullets to fire-form the cases after in my Contender.
Thought that had to be the easiest "wild cat" ever and the brass was dirt cheap