Since genotype imputation was introduced, researchers have been relying on the estimated imputation quality from imputation software to perform post-imputation quality control (QC). However, this quality estimate (denoted as Rsq) performs less well for lower frequency variants. We recently published MagicalRsq, a machine-learning-based imputation quality calibration metric, which leverages additional typed markers from the same cohort and outperforms Rsq as a QC metric. In this work, we extended the original MagicalRsq to allow cross-cohort model training, named MagicalRsq-X. We removed the cohort-specific estimated minor allele frequency and additionally included LD scores and recombination rates as variant-level features. Leveraging whole genome sequencing data from TOPMed, specifically participants in BioMe, JHS, WHI and MESA studies, we performed comprehensive cross-cohort evaluations for European and African ancestral individuals based on their inferred global ancestry with the 1000 Genomes and HGDP data as reference. Our results suggest MagicalRsq-X outperforms Rsq in almost every setting, with 7.3-14.4% improvement in squared Pearson correlation with true R2, corresponding to 85-218K variant gains. We further developed a metric to quantify the genetic distances of a target cohort relative to a reference cohort and showed that such metric could largely explain the performance of MagicalRsq-X models. Finally, we found that MagicalRsq-X saved 9-53 GWAS variants in one of the largest blood cell traits GWAS results that would be missed using the original Rsq for QC. In conclusion, MagicalRsq-X shows clear superiority for post-imputation QC and can greatly benefit genetic studies by rescuing well-imputed low frequency and rare variants.