I'm going to assume your settings files are JSON objects.
As seen here, when JSONCpp parses a file, it clears the contents of the root node. This mean that trying to parse a new file on top of the old one won't preserve the old data. However, if you parse both files into separate Json::Value nodes, it's straight forward to recursively copy the values yourself by iterating over the keys in the second object using getMemberNames.
// Recursively copy the values of b into a. Both a and b must be objects.
void update(Json::Value& a, Json::Value& b) {
if (!a.isObject() || !b.isObject()) return;
for (const auto& key : b.getMemberNames()) {
if (a[key].isObject()) {
update(a[key], b[key]);
} else {
a[key] = b[key];
}
}
}