The present disclosure provides methods of amplifying and sequencing DNA, comprising: extracting cell-free DNA from a blood, plasma, serum or urine sample of a transplant recipient who has received transplantation of one or more organs including simultaneous or sequential transplantation of multiple organs, wherein the extracted cell-free DNA comprises donor-derived cell-free DNA and recipient-derived cell-free DNA; performing targeted amplification at 200-50,000 target loci in a single reaction volume using 200-50,000 primer pairs, wherein the target loci comprise polymorphic loci and non-polymorphic loci; sequencing the amplification products by high-throughput sequencing to obtain a sequencing reads and quantifying the amount of donor-derived cell-free DNA and the amount of total cell-free DNA based on the sequencing reads; and determining whether the amount of donor-derived cell-free DNA or a function thereof exceeds a cutoff threshold indicating transplant rejection or graft injury.