The control of gene expression sometimes entails the folding of DNA into looped structures mediated by the binding of protein. Although the literature abounds with examples of single DNA loops induced by the attachment of sequentially distant genetic elements on a common protein core, recent studies have demonstrated the occurrence of multiple loops formed by three or more remote, protein-anchored sites. For example, the Escherichia coli Gal repressor has the ability to form oligomeric structures leading to higher-order helical protein pathways that can secure multiple chromosomal connections. Moreover, several novel experimental investigations have highlighted the role of bridging proteins, such as the macrodomain Ter protein (MatP) and the histone-like structuring protein (H-NS), in chromosome condensation and organization. These proteins are thought to be able to bridge distant DNA sites and to participate in the folding of the bacterial genome. We are examining the entanglement of DNA loops that attach to such proteins with the help of a novel energy minimization method associated with traditional Monte Carlo approaches. We focus on the multiple loops that can be induced by oligomeric Gal assemblies and report the relevant energy landscapes and topological and statistical properties as functions of the number of Gal repressors and the chain lengths of the different loops. In addition, we take advantage of the fact that our optimization method accounts for the presence along DNA of bound ligands to reveal how the binding of architectural proteins (e.g., the Escherichia coli histone-like HU protein) can ease or suppress the formation of such loops. Finally, we examine the influence of MatP and H-NS on the conformation and fluctuations of DNA minicircles to understand how these proteins may contribute towards the formation of topological domains.