I had two toilets back to back, using a fixture cross and a shared 2" vent in the last house.
Neither toilet affected the other toilet.
It could be a venting issue.
Have a common wall with 1.6 gal toilet on one side and old 4-5 gal toilet on the other side. Flush of 1.6 gal causes drain of bowl water in 4-5 gal toilet by approx. 1/2 inch per flush. Vent on roof is clear - did this week with snake - nothing found blocking. Just suction is pulling it at 1/2 inch per 1.6 gal flush and by the end of the day hardly any water is left in 4-5 gal toilet. Very annoyed. Any suggestions short of tearing the wall out for 2 vents? THX.
Agree with Terry, I think you have a venting problem.