  In our previous study of Neptune's 4:7 mean motion resonance (MMR), we
discovered that its resonant angle can only librate within a specific
eccentricity ($e$) versus inclination ($i$) region, determined by a theoretical
limiting curve curve (Li et al. 2020). This ``permissible region'' is
independent of time and encompasses the entire possible stable region. We now
generalize this theory to investigate all high-order MMRs embedded in the main
classical Kuiper belt (MCKB). We first consider the 2nd-order 3:5 MMR in the
framework of planet migration and resonance capture, and have further validated
our limiting curve theory for both captured and observed 3:5 resonators. It
suggests that only the $(e, i)$ pairs inside the individual permissible regions
should be chosen as initial conditions for studying the in-situ evolution of
high-order resonators. With such a new setting, we proceed to explore the
long-term stability (for 4 Gyr) of different resonant populations, and our
simulations predict that: (1) the 3:5 and 4:7 resonators are comparable in
number, and they could have inclinations up to $40^{\circ}$; (2) the
populations of objects in the higher order 5:9, 6:11, 7:12 and 7:13 resonances
is about 1/10 of the 3:5 (or 4:7) resonator population, and nearly all of them
are found on the less inclined orbits with $i<10^{\circ}$; (3) for these
high-order resonances, almost all resonators reside in their individual
permissible regions. In summary, our results make predictions for the number
and orbital distributions of potential resonant objects that will be discovered
in the future throughout the MCKB.
