From your picture, I would go with a AWG if 4 levels should be possible,
or a simple digital output ...
followed by a line driver , depending on the needed output power (and maybe a comperator as preamp)
If you try to create the PWMs with three 555 your phase will be unknown.. (OK, it's possible to oscillate them in sync... but why do that if software can do it much better 😉 )
Greetings from Germany
Henrik
LV since v3.1
“ground” is a convenient fantasy
'˙˙˙˙uıɐƃɐ lɐıp puɐ °06 ǝuoɥd ɹnoʎ uɹnʇ ǝsɐǝld 'ʎɹɐuıƃɐɯı sı pǝlɐıp ǝʌɐɥ noʎ ɹǝqɯnu ǝɥʇ'