The Catholic church will, in the next 10-15 years, slide ever further into degeneracy. They will offer communion to ever more extracanonical groups, and make ever more overt reaches towards LGBTQIA, potentially allowing diocesan-level decisions of wether to allow same-sex attendance and communion (though probably not marriage just yet).
At the same time, the Orthodox patriarch Bart will die and be replaced by the current archbishop of America, Elpi. Elpi is already pissing off Orthodox by loosening the requirements for communion, but most know he is the most likely successor to Bart.
The Orthodox church will scism along the Slavic/Greek lines that have been developing for decades now, with communion being denied to the other side. This will allow inter-communion and eventual formation of a new structure between Rome and Constantinople.
Tl;dr 20 years from now, Rome will be twice as degenerate, and have brought the traditional center of Orthodoxy under its heel. Traditional Catholic groups will have been denounced and excommunicated as the new Catholics basically complete their takeover. Orthodoxy will be left as a Slavic/Arab religion.
Thus is the fate of earthly churches which dare presume to call themselves the One True Way to God. They deserve it.