The DMG contains recommendations for the XP values of encounters that are supposed to help you create engaging but survivable combat encounters (page 82).
They work pretty well for low- and mid-level play. Unfortunately, for higher level play (Tier 3 and Tier 4) these recommendations are, to use a technical term, crap. At higher levels these encounters typically fail to pose adequate challenges for a competent adventuring party. I can confirm this from own experience, both as a player and as a DM.
As a DM, I have no qualms to throw monsters against high-level PCs that have a higher CR than the PCs' average level and I routinely ignore any multipliers for using more than one monster (and I tend to run a relatively low-magic equipment campaign).
Our DM does the same, regularly attacking us with multiple times the XP budget of a deadly encounter. We do have good magic items, but nothing over the top, no legendary items or such; our frontline fighter does not even have a magic weapon.
However, I think they are playing with fire by pushing ever farther beyond the guideline to break us -- at some point, the risk of a TPK becomes very real1.
I am therefore interested in understanding, what has worked in your campaigns as XP budgets for high level combat encounters (Tier 3, level 11-16), compared to what the DMG says? How many times more is OK in your experience? What in your experience has been too much? Have you been ignoring multipliers for multiple monsters routinely, and how did that work?
I appreciate that it would be very hard to give an exact answer for this, a lot will depend on the party composition and equipment. I am not looking for super-exact calculations, more for broad ranges.
1 In one recent encounter, our party of 3 characters of 12th level (XP budget for a "deadly" encounter per DMG: 13,500) was ambushed by an improved Hellfire Engine, Hobgoblin Warlord, 5 Hobgoblin Captains, 4 Hobgoblin Devastators, a Hobgoblin War Priest, Priest, Bard, and 30 normal Hobgoblins on fast vehicles. The naked XP value per DMG totals up to about 34,000 XP, without applying any multipliers. With multipliers for multiple monsters, it is 136,000, or more than 10 times the budget for a deadly encounter. We somehow managed to not only survive and escape, but also kill about half of the leadership and most of the rank-and-file Hobgoblins in the process. But this could have very easily, with one bad roll - resulted in the end of the campaign. The hellfire engine is removing the possibility of raising the dead.
