HER (hyper extension rule) is an expansion of ER (extension rule). The results of computing the union and difference set of two sets of maximum terms which are extended by two clauses respectively based on the hyper extension rule can be saved as EPCCL (each pair of clauses contains complementary literals) theories. In this paper, a parallelizable knowledge compilation algorithm for EPCCL theories, IKCHER, is proposed based on computing the intersection of maximum terms sets. The focus is placed on the research of parallel computing the intersection sets of multiple EPCCL theories based on HER, resulting in the design of the corresponding algorithm, PIAE (parallel intersection of any number of EPCCL). Through using the origin CNF formulae of EPCCL theories, another efficient merging algorithm imp-PIAE is proposed. Based on above methods two parallel knowledge compilation algorithms P-IKCHER and impP-IKCHER are constructed for EPCCL theories, utilizing the PIAE algorithm and imp-PIAE algorithm to merge multiple EPCCL theories respectively. Experimental results show that IKCHER algorithm has the best compilation quality of all EPCCL compilation algorithms. P-IKCHER algorithm does not improve the compilation quality and compilation efficiency of IKCHER while impP-IKCHER algorithms can maintain the compilation quality of IKCHER, and improve the compilation efficiency of IKCHER. When the number of CPU cores is 4, the compilation efficiency of IKCHER can be improved twice as much in the best cases.