1910 census Pontotoc Co, MS:
Shempert, Peter L., hd, 31, M(1) 9 yrs, b MS, MS, MS
" Anna L., wf, 26, M(1) 9 yrs, 5 ch, 5 lvg, b MS, MS, MS
" E_____, d, ?, b MS
" J.B., s, 6, b MS
" William C, 4, b MS
" B______, s, 3, b MS
" I______, d, 10/12, b MS
1920 census Pontotoc Co, MS:
Shempert, Peter L., hd, 42, b MS, MS, MS
" Anna, w, 37, b TX, MS, MS
" Elanore, d, 18, b MS, MS, TX
" Clarence, s, 14, b MS, MS, TX
" Vandie, s, 12, b MS, MS, TX
" Obion, d, 10, b MS, MS, MS [from here on mth of ch b MS]
" Elvy, s, 8, b MS
" Spurgeon, s, b MS
" Lenmon, s, 5, b MS
" Guy, s, 1 11/12, b MS
There are a couple of other Shemperts in the county on both censuses that look from age and born in MS like they probably are brothers to Peter.
1900 census Pontotoc Co, MS:
Combs, Lula, hd, b Feb 1824, 76, wid, 12 ch, ? lvg, b TN, NC, SC
Lambert, Annie, grd dau, b Sep 1883, 16, sgl, b TN, MS, AL
Shepherd(sic), Peter, boarder, b Jan 1889(sic), 21, sgl, b MS, MS, MS
Not real sure about grandmother's names, but the index shows these.Can't read how many children she had living, could be 8 or 0.Peter's name spelled Shepherd, and birth year read 1889, but probably should be 1879, to match his age.
I would look for land and probate records in that county, see if Annie/Anna shows up as an heir for a Lambert.When final sale of land was made outside of the family, all heirs would sign off, good way to pick up married names of female members of the family, too.
Also, look for probate and land records for the grandmother.It looks like she owns her own farm.
Happy Hunting (^_^)