Clothes washer back up into downstairs sink

I have a older house with iron waste pipes. The upstairs clothes washer two floors up is a front loader maytag. It drains water down a 2 or 2 1/2 inch pipe . The sink on the botton floor that backs up is on a run two feet from this verticle and 4 feet from the bottom of 7ft horrizontal run then to 4inch out the house. When I say backs up, it bubble a small amount into the sink. Once it did over flow and then I snaked the down side of this run but never 100%. Is there a one way check valve that can be spliced in just on the other side of the clean-out?

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