Philip A. Falcone, the brash hedge fund titan who once managed $26 billion before stumbling and running afoul of regulators, is pressing ahead on a new comeback effort, his second. His latest investment platform is a publicly traded company with $800 million in assets called HC2 Holdings. It has bought a couple of midsize businesses — an undersea cable installer and a steel fabricator — that are intended to generate cash to help support several smaller growth prospects that include operations in wireless services, natural-gas truck-fueling stations, life sciences, insurance and sports. For Mr. Falcone, the goal is to make...