Ok, two edits later…
This should work. The first time I tried it I think I had forgotten to set FileMode.Append on the oStream.
string test = "foo.txt";
var oStream = new FileStream(test, FileMode.Append, FileAccess.Write, FileShare.Read);
var iStream = new FileStream(test, FileMode.Open, FileAccess.Read, FileShare.ReadWrite);
var sw = new System.IO.StreamWriter(oStream);
var sr = new System.IO.StreamReader(iStream);
var res = sr.ReadLine();
res = sr.ReadLine();
sw.WriteLine("g");
sw.Flush();
res = sr.ReadLine();
res = sr.ReadLine();
sw.WriteLine("h"); sw.Flush();
sw.WriteLine("i"); sw.Flush();
sw.WriteLine("j"); sw.Flush();
sw.WriteLine("k"); sw.Flush();
res = sr.ReadLine();
res = sr.ReadLine();
res = sr.ReadLine();
res = sr.ReadLine();
res = sr.ReadLine();
res = sr.ReadLine();