  We describe a round robin scheduling problem for a competition played in two
divisions, motivated by a scheduling problem brought to the second author by a
local sports organisation. The first division has teams from 2n clubs, and is
played in a double round robin in which the draw for the second round robin is
identical to the first. The second division has teams from two additional
clubs, and is played as a single round robin during the first 2n+1 rounds of
the first division. We will say that two clubs have a **common fixture** if
their teams in division one and two are scheduled to play each other in the
same round, and show that for n>1 the maximum possible number of common
fixtures is 2n^2 - 3n + 4. Our construction of draws achieving this maximum is
based on a bipyramidal one-factorisation of K_{2n}, which represents the draw
in division one. Moreover, if we additionally require the home and away status
of common fixtures to be the same in both divisions, we show that the draw can
be chosen to be balanced in all three round robins.
