DNA-My Heritage has a suggested Theory of Relativity between LaMyra Morton, a descendant of Elizabeth Shetter Coffelt and a descendant of Catherine Shetter Johnson. If proven to work, the matches would be 5C.
Sources
See also:
Brian Liedike - Family 18 - Rootsweb
Ancestor Chart of Darlene Anderson, Rouge River, Oregon
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DNA Connections
It may be possible to confirm family relationships with Catherine by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Catherine: