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Dense passage retrieval (DPR) models show great effectiveness gains in first stage retrieval for the web domain. However in the web domain we are in a setting with large amounts of training data and a query-to-passage or a query-to-document retrieval task. We investigate in this paper dense document-to-document retrieval with limited labelled target data for training, in particular legal case retrieval. In order to use DPR models for document-to-document retrieval, we propose a Paragraph Aggregation Retrieval Model (PARM) which liberates DPR models from their limited input length. PARM retrieves documents on the paragraph-level: for each query paragraph, relevant documents are retrieved based on their paragraphs. Then the relevant results per query paragraph are aggregated into one ranked list for the whole query document. For the aggregation we propose vector-based aggregation with reciprocal rank fusion (VRRF) weighting, which combines the advantages of rank-based aggregation and topical aggregation based on the dense embeddings. Experimental results show that VRRF outperforms rank-based aggregation strategies for dense document-to-document retrieval with PARM. We compare PARM to document-level retrieval and demonstrate higher retrieval effectiveness of PARM for lexical and dense first-stage retrieval on two different legal case retrieval collections. We investigate how to train the dense retrieval model for PARM on limited target data with labels on the paragraph or the document-level. In addition, we analyze the differences of the retrieved results of lexical and dense retrieval with PARM.