It sounds like what you really want is a psi build that also happens to have some melee ability. You should probably know that, for example, Cryo Shield and Exothermic Aura can't coexist; whichever one you cast second will automatically cancel the first one, because heat and cold abilities don't play well together.
Expedition brings two really good psi weapons into the game, but they're both spears, so you might want to consider being slightly less tanky, and slightly higher strength, so you can go spear&shield.
Since you're going to be closing to melee range regularly, you don't want Tranquility - you want Psychosis so you can hit hard and fast while closing in. And since you want your psi abilities to be your main source of damage, you *need* Locus of Control. However, unlike Hulk above, I'd never suggest someone max out Thought Control; that's a huge waste of points for nearly no effective gain.
I'm assuming you'll be wearing a Muffled Uni-Psi Headband, and carrying the psi spear in one hand and a melee spear in the other, to switch between, since you'll have two main modes of damage output. If you really don't mind moving like a turtle, you could swap out Impale for Juggernaut and wear Riot Gear with a Psi Crab carapace(instead of, presumably, Psi Beetle), which would give you just enormous defensive boosts.
SInce you'll have psi as your principle damage source, you're going to be able to get by with skipping a lot of things that normal melee-focused builds can't do without; some Dodge, some Evasion, maybe Uncanny Dodge and Escape Artist. You can do without any of those things because psi is going to give you alternate paths to those sorts of defenses.
So here's my suggestion for you:
https://underrail.info.tm/build/?HgsDAwcDDAcAHgDCoAAAAFVaAABBWigyUEvCoMKgSzcAQVAoKywUKmUuwpQhwodpEsKvwqvCsmJ6378This build will let you run around with ~20% dodge/evasion from your sustained TM ability; it'll let you alpha strike with huge Psionic Mania hits (and if you're using Pyrokinesis or ThermoD, which you should probably be, Pyromania will give you huge bonus damage DoTs and fears on living targets) and then quickly stack defenses with Thought Control mirror images, LoC+Enrage group attacks, you can debuff ranged enemies to near uselessness. The bonus telekinetic damage will make your TK punches really very painful (especially if you've gone ahead and made your psi headband with the TK Punch module) so you'll have a brutal single-target damage option. And, because you're going spears rather than swords, you're going to be able to equip the best psi weapon in the game.
You may want not to worry about using spears in the early part of the game; start your character with 10 Will, put your level 4 and level 8 stat points into Will, and play your first 16 levels as pure psi, but with a melee weapon of some sort equipped. If you do want to use spears early on, you probably should go with metal armor over riot gear, or else take Iron Grip rather earlier - but since melee is only a support damage source, I built the character to be pure psi early on then branch into melee around level 20 or so. If you're playing Classic XP, that'll be no trouble, but if you're playing Oddity it may mean that you'd need to explore a lot and pick up all the easy levels in UnderRail before going on the expedition to Black Sea.
I think, for a mostly-psi build that also wants to be a tanky melee type, this should be DOMINATING viable.
EDIT: I should add that this build does assume you'll be cooking your own Hypercerebrix so you can make MKIV grenades, hit all the necessary Mercantile thresholds as well as - if you wish - the 130 Hacking check in DC, and still craft top-tier Riot Gear and Energy Shields.
