You should generally be more concerned about managing overall fatigue, rather than local muscle fatigue.
Fitness adaptations occur in response to the accumulation of fatigue through exercise, but not all exercises are equally fatiguing. Movements that use lots of muscles, called compound movements, are the most fatiguing. Naturally, using more muscle mass means using more metabolic resources to get the job done. So exercise like the barbell back squat and deadlifts from the floor are highly fatiguing exercises. They consume lots of resources and impose higher recovery demands than any other movements because the prime movers are huge muscles (quadriceps, hip extensors), and they both use the entire musculature of the back for support. Lots of muscles, lots of fatigue.
In contrast, movements that use less muscles or smaller muscles do not impose the same amount of fatigue or recovery demands. Think about it, what's more likely to leave you on the floor of the gym? Five sets of five on back squat with 85% of your 1RM or five sets of five on leg extensions with 85% of your 1RM? You could probably do the leg extensions on 60 seconds rest without really elevating your heart rate, but the back squats are going to be tough, even with plenty of rest.
So what I do with my training is I spread my big compound movements out across the week, and fill in the rest with lower fatigue exercises. This keeps my overall fatigue about the same workout to workout, but different muscle groups get fatigued more or less in different workouts.
Lets break it down for a three day per week program just as an example of these principles.
Monday
First day of the week, I'll hit the exercise that fatigues me most after I've recovered over the weekend: barbell back squats. For me, this looks like 4 to 6 sets of 4 to 6 reps with a fairly challenging load, somewhere in the 75-80% 1RM range. By the end of this, I'm pretty beat up, but I still need to do some other work.
Next I will do a lower fatigue pressing movement, something like a overhead press or feet up bench. OHP uses small muscles (mostly delts) so the fatigue cost is minimal. Feet up bench forces you to limit the load because you cannot use leg drive, and does a good job of isolating the pecs, again, smaller muscles means less fatigue.
Then I will do some kind of pulling movement, like cable rows or dumbell rows, to hit my back without imposing any significant fatigue. The back has lots of muscles, but by doing a machine or dumbell row, you limit the demands put on all the supporting musculature. Something like a barbell row is not what I'm looking for here - it places significant demands on the trunk and legs to support the position for rowing a barbell.
Wednesday
The big squats are done, and I'm still a bit tired from them two days later, so today I'm doing my main press, the flat barbell bench press. I'm going heavy, using full leg drive, so it really is a full body exercise. It isn't as fatiguing as back squats, but it still takes a good bit out of me.
Since the bench wasn't as fatiguing as Monday's squats, I've got more room to work, so I might do some medium fatigue leg movement, some sort of squat variation. We can lower the fatigue cost of the squat by modifying the movement in a way that limits the load. For example, I might do a Bulgarian Split Squat or a Barbell Lunge. These are single leg movements, so they greatly limit the amount of weight you put on the bar, which means less overall fatigue, even though they can easily tap out your quads and glutes pretty quickly.
Finally, I might throw in some extra shoulder work, this time even lower fatigue than the overhead press, something like light dumbbell lateral raises.
Friday
Deadlift day. Like Monday, I'm going heavy, and I'm not going to have much left in the tank when I'm done. Once I've finished deadlifting, it's going to be isolation movements. I'll hit the quads with leg extensions, hit the chest with incline dumbbell press, might hit the back with reverse flies, etc.
Anyway, the idea here is that you manage fatigue by spreading out higher fatigue movements, arranging your exercise selection so that the total fatigue each day adds up to be about the same, and hitting all your muscle groups two or three times per week, maybe more on the smaller muscles.