One way is to go to UK and stay 91 days.
Bosnia Herzegovina has a 90/180 rule similar to Schengen, but it isn't part of Schengen. BUT, since the day you cross is counted on both sides, if you go back into Schengen on the 90th day, you'd technically have 91 days in your Schengen 180. But you can't stay in Bosnia because you would have 91 days there. So to be legal, you'd have to find some other non-Schengen country to go to for at least one day.
Supposing a US citizen wants to travel on foot or bicycle (and if there were no COVID issues), what routes could he use to stay in Europe legally without having to hassle with visa paperwork?