I made a coaxial (phono socket type) to optical converter once with not many components, was 11 years ago and now they are about £6 on CPC as checked that company for the switcher box with no joy.
I am not sure they exist, spent 20 minutes looking and if google is a no then not much chance!.
Does the amp have a coaxial digital input as wel then could convert one bit of kits output to that and use that amp input not used (if it exists, guess not or you would).
The nasty silver grey plastic switchers are £5 each so could plug 3 into 1 of them , take out put to another and the 2 other audio/ visual kit or games machine to that as well so 2 boxes, messy but works.
I have a surround sound amp last Dec and all the bits freeview Hard disk rec, bluray and telly go into that on HDMI and the correct HDMI on the telly, only number 2 outputs telly sound and it all goes, has 2 optical inputs as well that 1 is used for digital radio.
Newer amps, loads of inputs!.
and no need for nasty red, white and yellow plugs, digital all the way.
Would the 2, 3 way boxes daisy chained be a winner, if not a bit messy.