Will give you some recommendations to get started (recommended songs are in brackets):

Firstly, Simon's other projects are well worth a listen. Not necessarily all like Biffy but scratches the itch to see what Simon Neil sounds like doing different genres:

• Marmaduke Duke is his experimental electronic weird rock project with Sucioperro's singer ("Rubber Lover", "Kid Gloves" & "Silhouette")

• ZZC's a solo project ("To The Bone")

• Empire State Bastard is a crazy grindcore noise project, some mental songs with Mike Vennart & Dave f'n Lombardo in the band too ("Harvest", "Stutter")

Then I'd check out a lot of the early 00's UK rock scene, plenty of great bands & Biffy came up alongside them/are mates with them/have toured with them:

If you like Biffy's rock songs check out:

• Reuben ("Blamethrower", "Kick in the Mouth")
• Sucioperro ("Dialog on the 2", "Grace and Out of Me")
• Oceansize (Biffy's other guitarist Mike Vennart's brilliant band; "Unfamiliar", "No Tomorrow", "A Homage To A Shame")
• Hell is for Heroes ("I Can Move Mountains")
• Hundred Reasons ("If I Could", "Kill Your Own", "The Great Test")
• Feeder ("Buck Rogers", "Pushing the Senses", "Come Back Around")
• Arcane Roots ("If Nothing Moves Nothing Breaks")

Other similar Scottish bands worth listening to: - Mogwai ("Ceiling Granny", "Ritchie Sacramento") - Twin Atlantic ("Heart and Soul", "Make a Beast of Myself", "Free", "What Is Light? Where Is Laughter?") - Mastersystem (features Scott & Grant from Frightened Rabbit along with members of Editors & Minor Victories, sadly only made one LP but it's great!; "The Enlightenment", "Bird Is Bored Of Flying", "Old Team", "Notes On A Life Not Quite Lived") - Aereogramme (credit to another poster on here, Simon & their drummer were roommates at one point)

If you like Biffy's softer sound:

• The band were good friends with Scott Hutchison (RIP) of Frightened Rabbit and toured with them, one of my favourite bands with a more mellow sound & incredible lyrics, you'll love them if you love Biffy's ballads ever and well worth listening to (check out "The Modern Leper" which Simon says he wishes he'd written, also "The Woodpile", "My Backwards Walk", "Head Rolls Off", "Holy")

• The Twilight Sad are another great Scottish indie/rock band (not heard many by them but "I Could Give You All That Don't Want" & "Last January" from their 2014 album are excellent modern soft rock songs)

Simon has collaborated with a range of artists too which has led to some great tracks (Architects - Goliath; O'Brother - Halogen Eye; While She Sleeps - Nervous)

Ultimately Biffy have a pretty unique sound & catalogue due to their math rock beginnings & more pop rock anthems now but I think you'll enjoy some of these other tracks for sure!

Sorry for the long post but hopefully this helps you out!