This paper is a sequel to an earlier paper devoted to multiple, multicycle nova evolution models (Prialnik & Kovetz, Paper I), which showed that the different characteristics of nova outbursts can be reproduced by varying the values of three basic and independent parameters: the white dwarf mass, MWD, the temperature of its isothermal core, TWD, and the mass transfer rate, . Here we show that the parameter space is constrained by several analytical considerations and find its limiting surfaces. Consequently, we extend the grid of multicycle nova evolution models presented in Paper I to its limits, adding multicycle nova outburst calculations for a considerable number of new parameter combinations. In particular, the extended parameter space that produces nova eruptions includes low mass transfer rates down to 5 × 10-13 M☉?yr-1 and more models for low TWD. Resulting characteristics of these runs are added to the former parameter combination results to provide a full grid spanning the entire parameter space for carbon-oxygen white dwarfs. The full grid covers the entire range of observed nova characteristics, even those of peculiar objects, which have not been numerically reproduced until now. Most remarkably, runs for very low lead to very high values for some characteristics, such as outburst amplitude A 20, high super-Eddington luminosities at maximum, heavy element abundance of the ejecta Zej ≈ 0.63, and high ejected masses mej ≈ 7 × 10-4 M☉.
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