  We study a generalized interacting self-avoiding walk (ISAW) model with
nearest- and next nearest-neighbor (NN and NNN) interactions on the square and
cubic lattices. In both dimensions, the phase diagrams show coil and globule
phases separated by continuous transition lines. Along these lines, we
calculate the metric $\nu_t$, crossover $\phi_t$ and entropic $\gamma_t$
exponents, all of them in good agreement with the exact values of the $\Theta$
universality class. Therefore, the introduction of NNN interactions does not
change the class of the ISAW model, which still exists even for repulsive
forces. The growth parameters $\mu_t$ are shown to change monotonically with
temperature along the $\Theta$-lines. In the square lattice, the $\Theta$-line
has an almost linear behavior, which was not found in the cubic one. Although
the region of repulsive NNN interactions, with attractive NN ones, leads to
stiff polymers, no evidence of a transition to a crystalline phase was found.
