Looking at last year as a frame of reference...
Sat 9 Sep - PL @ Everton (7 Sat, 2 Sun, 1 Mon [West Ham vs Huddersfield] games)
Wed 13 Sep - UCL vs Dortmund
Sat 16 Sep - PL vs Swansea (1 Fri [Bournemouth vs Brighton], 7 Sat, 2 Sun games)
Tue 19 Sep - Cup vs Barnsley
Sat 23 Sep - PL @ West Ham (8 Sat, 1, Sun, 1 Mon [Arsenal vs West Brom] games)
Tue 26 Sep - UCL @ APOEL
Sat 30 Sep - PL @ Huddersfield (7 Sat, 3 Sun games)
Int'l Break
Sat 14 Oct - PL vs Bournemouth (7 Sat, 2 Sun, 1 Mon [Leicester vs West Brom] games)
Tue 17 Oct - UCL @ Madrid
Sun 22 Oct - PL vs Liverpool (1 Fri [West Ham vs Brighton], 7 Sat, 2 Sun games)
Wed 25 Oct - Cup vs West Ham
Sat 28 Oct - PL @ ManU (7 Fri, 2 Sun, 1 Mon [Burnley vs Newcastle] games)
Wed 1 Nov - UCL vs Madrid
Sun 5 Nov - PL vs Palace (6 Sat, 4 Sun games)
Seems like PL schedules 1 game for Friday or Monday most weeks although it was usually shit teams last year. Doesn't seem to be any correlation between Champions League / League Cup day and Premier League day (Spurs had Wed / Sat, Tue / Sat, Tue / Sun and Wed / Sun above).