I have put together the schedule below which I think will work. The fixed teams are numbered 1 to 16, the first four groups in each row are the teams that meet together each month, the square brackets contain the 4 teams who host each month.
SEP {16 4 6 7} { 1 2 3 5} { 8 12 14 15} { 9 10 11 13} [2 6 10 14]
OCT {14 11 5 7} { 8 9 2 4} { 6 3 13 15} {16 1 10 12} [1 7 9 15]
NOV {13 2 12 7} {14 16 9 3} { 5 10 4 15} { 6 8 1 11} [3 4 11 12]
DEC {11 16 2 15} {12 5 6 9} { 3 8 10 7} { 4 13 14 1} [5 16 13 8]
JAN { 2 6 10 14} { 1 7 9 15} { 3 4 11 12} { 5 16 13 8} [3 6 8 9]
FEB { 8 4 14 7} { 9 2 11 5} {16 12 6 15} { 1 10 3 13} [5 7 10 12]
MAR { 9 13 16 7} {10 11 4 6} { 1 5 8 15} { 2 3 12 14} [1 11 14 16]
APR { 2 6 1 7} { 3 4 5 16} {10 14 9 15} {11 12 13 8} [2 4 13 15]
By the end of January every team should have met every other team exactly once. Note that every teams hosts once in the 1st four rounds, and once in the 2nd four rounds, team 8 ends up hosting twice in a row.
