"Back-end" DTI includes your proposed mortgage payment plus all other minimum debt payments (car, credit cards, student loans, alimony, existing mortgages). "Front-end" DTI is just housing over income.
Conventional loans typically cap at 43% DTI for best pricing, 50% with compensating factors. FHA goes up to 57% with factors. Jumbo programs tighten to 43% or less. Non-QM programs often extend to 50%+.
If your DTI is the constraint, three levers: (1) pay down a debt balance before close, (2) extend a different loan term to reduce the monthly payment, (3) consider a different program with a higher DTI ceiling.