What size of tyres can you run on a 404 axle without breaking anything?

wrap the rims in a small sheet of rubber, park it in the garage... never drive it!

I guarantee it won't break.

Way too many factors missing to answer your question.
How old are the axles, how many miles, were they pulling a train or sitting under a fire dept. parade truck? Are they original or factory reconditioned?

How much power are going to them? V8? Diesel?

If you are running stock Mog power levels (100-200 HP) I do not think a set of axles in excellent condition could not run 44-49" tires on most surfaces. Bouncing violently with 400 horses on tap will kill good axles with 40" tires.

A toyota 4cyl, with good gearing, I would run ANY tire I could gear to run.

Diesel, it will be around 150 hp en 400NM.
I was thinking at 42" tires.

Your 42's should be good.