The isobaric nucleon model of pion production in nucleon-nucleon and pion-nucleon collisions has been extended to include the effect of the higher resonances in the isotopic spin $T=\frac{1}{2}$ state of the pion-nucleon system, in addition to the effect of the well-known low-energy $T=\frac{3}{2}$ resonance which has been previously investigated. The higher $T=\frac{1}{2}$ resonances are centered at incident pion energies of 600 and 880 Mev, and thus correspond to isobar masses ${m}_{\mathrm{I}}=1.51 \mathrm{and} 1.68$ Bev, respectively, as compared to ${m}_{\mathrm{I}}=1.23$ Bev for the $T=\frac{3}{2}$ resonance. For the inelastic pion-nucleon interactions, calculations of the various pion and recoil nucleon energy spectra have been carried out for incident pion energies ${T}_{\ensuremath{\pi},\mathrm{inc}}=1.0, 1.4, \mathrm{and} 2.0$ Bev. We have considered both single and double pion production by the incident pion, corresponding to two-pion and three-pion final states, respectively. General equations for the center-of-mass energy spectra of the final-state pions and nucleons have been obtained for all single and double pion production reactions from both ${\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{-}p$ and ${\ensuremath{\pi}}^{+}\ensuremath{-}p$ collisions. The results of the present extended isobar model at ${T}_{\ensuremath{\pi},\mathrm{inc}}=1.0$ Bev are in reasonable agreement with the combined data from three experiments on ${\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{-}p$ interactions in the region of 1.0 Bev incident energy. The $Q$ value distributions for pion-nucleon and pion-pion pairs have been calculated for single pion production at ${T}_{\ensuremath{\pi},\mathrm{inc}}=1.0$ Bev. The present extension of the isobar model can also be used to treat up to four-pion final states in $\ensuremath{\pi}\ensuremath{-}N$ interactions, and up to eight-pion final states in $N\ensuremath{-}N$ interactions.For pion production in nucleon-nucleon collisions, we have obtained the branching ratios for all pion production reactions which involve the isobaric states ${{N}_{1}}^{*}$, ${{N}_{2a}}^{*}$, and ${{N}_{2b}}^{*}$, corresponding to the $T=\frac{3}{2}$ and $T=\frac{1}{2}$ resonances. General equations for the energy spectra of the final-state pions and nucleons have been derived for all single- and double-pion production reactions from both $p\ensuremath{-}p$ and $n\ensuremath{-}p$ collisions. Calculations of the various pion and nucleon energy spectra have been carried out for incident nucleon energies of 2.3 and 3.0 Bev. For the processes of pion production in antinucleon-nucleon interactions which do not result in annihilation, it has been assumed that an anti-isobar ${{\overline{N}}_{\ensuremath{\alpha}}}^{*}$ can be produced, which is the antiparticle of the isobar ${{N}_{\ensuremath{\alpha}}}^{*}$. Specific results have been obtained for both single and double pion production in $\overline{p}\ensuremath{-}p$, $\overline{p}\ensuremath{-}n$, and $\overline{n}\ensuremath{-}p$ collisions.