Hi Mollydog,
My wife's maiden surname is Menzies and her grandfather was Thomas Warden Menzies (John's younger brother). Their father John Menzies snr, was married twice ( 1st to Marion Lumsden and later to Isabella Warden and between them had a total of 17 children.
Female siblings were Mary, Rachel, Margaret, Marion* and Jane*. Perhaps your Grandmother was one of these sisters. They were all half sisters to Thomas and full sisters to John jnr.
* died in infancy
Hope this helps a little and should you need any further info please let me know.
Regards