Other newer movies like BTBR...

Yes, that's what I'm here for...though you'll have to travel back in time quite a ways to find the director's influences. The wiki on this film is actually pretty informative so go check that out.

Mulholland Dr. (2001)
Fear X (2003)
The Wild Blue Yonder (2005)
Bug (2006)
Youth Without Youth (2007)
Slipstream (2007)
Valhalla Rising (2009)
Biutiful (2010)
Tron: Legacy (2010)
Only God Forgives (2013)
Magic Magic (2013)
A Field in England (2013)
The Wait (2013)
Under the Skin (2013)
Lost River (2014)

On second thought I don't know what you mean by "like" because there just ain't much like it... Visually, go with Tron and atmospherically The Wait or Mulholland.

For older stuff definitely check out Exorcist II and The Keep.

For visual style:

Amer
The Strange Color of Your Body's Tears
Horsehead

With a similarly strong sense of visual style, combined with 70s fetishism, sound design, music, and horror, Berberian Sound Studio is a film to see.

Arguably better than BTBR, but less atmospheric.

You can't be more horrific than life itself. - Francis Bacon

You could check out the following:

1) Berberian Sound Studio (2012)
2) Gozu (2003)
3) Multiple Personality Detective Psycho (2000)

Baskin (2015), a red&blue trippy gory horror from Turkey. Just replace the Scanners influences in BTBR with Hellraiser.

You know I watched STRANGER THINGS which is also set in 1983 and it made me think of BEYOND THE BLACK RAINBOW. I know they are different in style, but they both had a girl with ESP powers, a lab setting that messed with other realities, some tripped out scientists, and cool music. Maybe more things but that is what I picked up.

You should really check Coherence(2013) and there is one older movie that reminds me much of BTBR called Suspiria (1977), which has also a killer soundtrack and visuals...

I would guess that someone who enjoyed the aesthetic of Beyond the Black Rainbow would also at least somewhat enjoy Synchronicity 2015.