A client received an amended Schedule K-1 for the 2020 tax year today. I have previously E-filed an amended return for him for tax year 2021, and paper filed an amended California return for 2021. His CA return had more than two Forms 6804 so it would not E-file. (note ProSeries did not alert me to this restriction/error until after I had tried to E-file the CA amended return and it was rejected. Also, Technical Support did not know of this restriction either.)

Is there any restriction on E-filing the federal 1040X for TY 2020 in this calendar year?

It appears the CA original return was not E-filed because the client had more than 97 entries on Form 3801 (Passive Activity Loss Limitations). I'm assuming that will prohibit E-filing of the CA 2020 amended return, so a paper filing will be needed for CA.