A growing number of linked data sources are published on the Web. They form a single huge data space referred to as the Web of data. These data sources contain both the data and the schema describing them, but the data is not constrained by this schema. Indeed, two instances of the same class may be described by different properties. This flexibility for describing the data eases their evolution, but it comes at the cost of losing the description of the data, which can be useful in many contexts. The different structures of a class represent its versions. These versions provide useful information on property co-occurrence for a class, but their discovery can be very costly, and even impossible because the data sources are remote. Furthermore, they may have some access limitations, either on the query execution time, or on the number of queries, or on the size of the results.In this paper, we present SchemaDecrypt++, a novel approach for the parallel discovery of a versioned schema for a remote data source. Our approach discovers the versions on-line, without uploading or browsing the data source. Broadly speaking, SchemaDecrypt++ allows to discover co-occurrences between properties from any set of properties: (i) specified by the user; (ii) describing the instances of a class or (iii) specified in the schema. SchemaDecrypt++ relies on our previous approach for schema discovery, SchemaDecrypt; in the present work we introduce a new strategy of parallelization of class version exploration, based on the discovery of a set of occurrence rules between the properties of the class. This strategy enables to overcome the source querying restrictions, the combinatorial explosion of the candidate versions and it improves the performances. We present some experimental evaluations on DBpedia to demonstrate the effectiveness of our approach.