Primitive Pythagorean Triples

Hello,

Are there any primitive Pythagorean triples where the one hypotenuse has
more than the two values for the other two sides? So, in the case of the
3, 4, 5 right triangle, there's the two possible arrangement of sides 3,
4, 5 and 4, 3, 5. Are there any triangles with more than two arrangements
for the one single size of hypotenuse?

I haven't found any, looking at hypotenuse up to 10,000, but don't
immediately see why there couldn't be solutions of: a, b, h; b, a, h; c,
d, h and d, c, h.

Apologies if this is inappropriate here. My maths is okay, but just high-
school level, nothing more...

Thanks,
--
David Entwistle