Transformer winding

[j-po]

Ok gearheads, here's a tricky question:
I would like to wind my own power transformer using the existing primary and iron of a old hifi amp power transformer. Can I wind on any secondary or do the specs of the primary winding change depending on what is on the secondary? Like primary inductance...

Originally it had 80V AC on the secondary so 300V will be quite a change. The iron looks big enough to easily power a 2x6V6 so it would be a shame not to use it.

Comments are greatly appreciated.