Spectral lines from N-like ions can be used to measure the temperature and density of various types of astrophysical plasmas. The atomic databases of astrophysical plasma modelling codes still have room for improvement in their electron-impact excitation data sets for N-like ions, especially $R$-matrix data. This is particularly relevant for future observatories (e.g. Arcus) which will host high-resolution spectrometers. We aim to obtain level-resolved effective collision strengths for all transitions up to $nl=5d$ over a wide range of temperatures for N-like ions from O II to Zn XXIV (i.e., O$^{+}$ to Zn$^{23+}$) and to assess the accuracy of the present work. We also examine the impact of our new data on plasma diagnostics by modelling solar observations with CHIANTI. We have carried-out systematic $R$-matrix calculations for N-like ions which included 725 fine-structure target levels in both the configuration interaction target and close-coupling collision expansions. The $R$-matrix intermediate coupling frame transformation method was used to calculate the collision strengths, while the AUTOSTRUCTURE code was used for the atomic structures. We compare the present results for selected ions with those in archival databases and the literature. The comparison covers energy levels, oscillator strengths, and effective collision strengths. We show examples of improved plasma diagnostics when compared to CHIANTI models which use only distorted wave data as well as some which use previous $R$-matrix data. The electron-impact excitation data are archived according to the Atomic Data and Analysis Structure (ADAS) data class it adf04 and will be available in OPEN-ADAS. The data can be used to improve the atomic databases for astrophysical plasma diagnostics.
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