The MM (and DMG) are terrible at monster design to begin with. One might need guidance on CR and Encounter Design to appropriate balance an encounter for a Level UP! party, but that kind of work is necessary anyway, given player skill level and, again, the relative imbalance within the MM already.
So if you go back to the DMG rules for CR, the system is pretty simple.
XP is roughly HP*DPR*(1 + 0.1 * (AC+ATK-13))/5
Then round it a bit.
Or, in simple terms, XP is threat times soak times a constant.
If you spread a PCs resources over an adventuring day (so, give them 2 short rests, assume they burn all of their HD and deal damage with all of their resources, give them 9ish encounters of at least 20 rounds, or other similar assumptions) you get an "XP" value for PCs.
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Now, if you want to combine monsters, the DMG has a "add up 3 monsters XP, then multiply by 2" rule. That is annoying.
Instead, raise monster XP to the .67th power (+/- 0.02). Now XP adds up linearly.
If you divide that XP^.675 by 28.5, you get a value that tracks a slightly modified CR.
You can derive the result of XP^0.675 / 28.5 (the "linear" encounter building value) from CR directly.
CR 1/8 becomes 0.25, CR 1/4 becomes 0.5, CR 1/2 becomes 0.75 and CR 1 becomes 1.25.
Add an extra +1 to your CR at level 5 and 11. (there are bumps on the chart).
If CR > 10, add CR-10 (so you gain 2 points per CR after CR 11, and 3 at CR 11).
If CR > 20, add CR-6 (so you gain 8 points per CR after 20)
You get this:
0.25 / 0.5 / 0.75 / 1.25 for CR 1/8 to 1.0.
Then 2, 3, 4 for CR 2-4.
Then 6, 7, 8, 9, 10, 11 for CR 5-10.
Then 14, 16, ..., 32 for CR 11 to 20.
Then 40 ... 112 for CR 21 to 30.