Abstract Close galaxy flybys, interactions during which two galaxies inter-penetrate, are frequent and can significantly affect the evolution of individual galaxies. Equal-mass flybys are extremely rare and almost exclusively distant, while frequent flybys have mass ratios $q=0.1$ or lower, with a secondary galaxy penetrating deep into the primary. This can result in comparable strengths of interaction between the two classes of flybys and lead to essentially the same effects. To demonstrate this, emphasise and explore the role of the impact parameter further, we performed a series of N-body simulations of typical flybys with varying relative impact parameters $b/R_{\mathrm{vir},1}$ ranging from $0.114$ to $0.272$ of the virial radius of the primary galaxy. Two-armed spirals form during flybys, with radii of origin correlated with the impact parameter and strengths well approximated with an inverted S-curve. The impact parameter does not affect the shape of induced spirals, and the lifetimes of a distinguished spiral structure appear to be constant, $T_\mathrm{LF} \sim 2$ Gyr. Bars, with strengths anti-correlated with the impact parameter, form after the encounter is over in simulations with $b/R_{\mathrm{vir},1} \leq 0.178$ and interaction strengths $S\geq0.076$ , but they are short-lived except for the stronger interactions with $S\geq0.129$ . We showcase an occurrence of multiple structures (ring-like, double bar) that survives for an exceptionally long time in one of the simulations. Effects on the pre-existing bar instability, that develops much later, are diverse: from an acceleration of bar formation, little to no effect, to even bar suppression. There is no uniform correlation between these effects and the impact parameter, as they are secondary effects, happening later in a post-flyby stage. Classical bulges are resilient to flyby interactions, while dark matter halos can significantly spin up in the amount anti-correlated with the impact parameter. There is an offset angle between the angular momentum vector of the dark matter halo and that of a disc, and it correlates linearly with the impact parameter. Thus, flybys remain an important pathway for structural evolution within galaxies in the local Universe.