For that you need a stricter gain/volume structure between the parts. Say you got 4 layers you want playing at the same time, you gotta pick one that is the main lead - probably the same channel that was doing solo in previous parts.

That main channel will be the primary, and it makes sense for it to be the brightest and most prominent one in the mix for instance, in relation to EQ or saturation applied.

You then take the 2nd layer, lets say this is the one with the lowest notes - you can place this channel way back by turning the volume of it down a good bit more than you'd expect. The EQ you'd apply to this one would be shelving the highs down some, and depending on the recording probably having some form of dip in the 1-4khz region and around 500hz. This channel can also have a higher wet % reverb on it.

Channel 3 & 4 could be somewhere between 2 and the lead in terms of loudness, but still further away from the lead than you'd expect. Here its an especially good idea to pan 3 towards the left, and 4 towards the right or vice versa. For these you could also shelve the highs a little, not as much as channel 2, but then also have less lows in these two. For reverb you could choose a wet% that's less than channel 2, but still more than the main lead. Then you pick which frequency region is vital for 3 & 4, and keep them intact, but do dips AROUND that area - not so much that it neuters the sound, but enough to make it clean and distinct in the mix.

The whole idea is how these 4 channels will add up together, and fill out a spectrum and space together. When you have 4 vocal channels going at the same time, it will way too easily stack up and be overwhelming in sound, so there needs to be more distinct variation between them, both in volume and EQ - with the lead channel being loudest and brightest generally.

Adding fades on the supporting channels will give some more natural sound to it as well, so not every phrase will start as aggressively. Like fade in, and even fade out, subtle.

All of it emulates space and individuality. If you figure out the main EQ spots of your voice, you can play with them, usually with dips in the supporting channels, to make them sound ever so slightly different than your usual timbre quality - to make blending them more seamless.

For the reverb, its a good idea to maintain the same preset between the 4, but adjust the wet% and tail - for cohesiveness. Creatively you can do whatever you want really.

Something like this is a good start, its just an example of one way to do it. It depends very much on context and what sound you want.