Please note that max RPM was up-rated, from 2700 RPM as, for example, in the well known DB-603A, to 3000. More rpm - more power. The C3 fuel enabled more boost, 2 ata was used on take off and up to 32600 ft (capable for 1930 PS there). The 'Fugmotoren und S.' book has the graph that shows the lines for 603 line, there is a caption 'DB 603N-MW Projekt 1945. The 603N endured a redesign, vs. the 603L for example. The inlet guide vanes were also incorporated, that device can further increase the power under rated altitude.
Two-stage compressor played as much as no role in take off performance, some designs (like P&W ones, for example) were capable to completely disconnect one stage in really low altitudes, so less power was being taken away from prop.