And I'm okay with that. Most really oddball 5e character build ideas fall into the "possible at a high cost in feats or multiclassing" column rather than being outright impossible. About the only thing you can't do is combine high level features from multiple classes, just because you cap out at 20th level.
Are most of these things a good idea? Not unless you're in a really low challenge campaign where everyone's aiming for a lower power level. One out of ten of these multiclass builds has a specific synergy that gets you equal or greater power to just playing a single class, and the other nine are a mess of conflicting and non-complimentary features. But if the DM allows, you have the freedom to make those characters without needing special rules hacks.