Despite the recent growth in the size of the Linked Data Cloud, the absence of links between the vocabularies of the sources has resulted in heterogenous schemas. Our previous work tried to find con-ceptual mapping between two sources and was successful in finding align-ments, such as equivalence and subset relations, using the instances that are linked as equal. By using existential concepts and their intersections to define specialized classes (restriction classes), we were able to find alignments where previously existing concepts in one source did not have corresponding equivalent concepts in the other source. Upon inspection, we found that though we were able to find a good number of alignments, we were unable to completely cover one source with the other. In many cases we observed that even though a larger class could be defined com-pletely by the multiple smaller classes that it subsumed, we were unable to find these alignments because our definition of restriction classes did not contain the disjunction operator to define a union of concepts. In this paper we propose a method that discovers alignments such as these, where a (larger) concept of the first source is aligned to the union of the subsumed (smaller) concepts from the other source. We apply this new algorithm to the Geospatial, Biological Classification, and Genetics do-mains and show that this approach is able to discover numerous concept coverings, where (in most cases) the subsumed classes are disjoint. The resulting alignments are useful for determining the mappings between ontologies, refining existing ontologies, and finding inconsistencies that may indicate that some instances have been erroneously aligned.