I'm having an issue with water overflowing from basement plumbing which is directly next to washing machine and under the kitchen. I have lived here for 7 yrs so it's a new issue.

Whenever I run a lot of water in kitchen or the washing machine drains, the water sprays out of the vertical pipe where the washing machine drain hose goes in.
I have snaked 2 parts of the plumbing: from clean out to floor drain and from floor drain to main. This has not solved the problem so my GUESS is its from the kitchen down to the clean out but my snake head is too large (to get down kitchen drain due to the screw in for the strainer) to try this.

Please help!
I cannot afford a plumber right now.

Disconnect the trap under the kitchen sink. Run your snake into the drain that comes out the wall under the kitchen sink.

Put bleach in the all the sinks.the lowest one first work up to the highest one pour slow let set for a time the longer the better then run hot water from the lowest up,you may use a few gl, but it will work .I do ti in my rentels all the time. Do it every few mts.to keep them open