using (var fs = new FileStream("test.txt",
            FileMode.OpenOrCreate, FileAccess.ReadWrite, FileShare.Read))
        {
            JsonSerializer serializer = new JsonSerializer();

            using (var sw = new StreamWriter(fs))
            using (var jtw = new JsonTextWriter(sw))
            {
                fs.Seek(-Encoding.UTF8.GetByteCount("]"),SeekOrigin.End);
                sw.Write(",");
                sw.Flush();
                serializer.Serialize(jtw, _data);
                sw.Write(']');
            }
        }

[{"Name":"ABC","Date":"2019-07-20T130924","X":456,"Y":-42},
[{"Name":"DEF","Date":"2020-01-20T130924","X":123,"Y":-12}]]

[{"Name":"ABC","Date":"2019-07-20T130924","X":456,"Y":-42},
{"Name":"DEF","Date":"2020-01-20T130924","X":123,"Y":-12}]