Some really good stuff in this thread, and these points raise some interesting questions about 5E's design space for non-combat options. I do wonder if this is a bit of a fool's errands, largely for the things that Quickleaf pointed out.
Beyond skills, there aren't a lot of design knobs that can be turned for non-combat. Giving the fighter Expertise is absolutely a quick and easy fix, and a decent one at that. But giving the fighter some additional skill bonuses continues down the path of watering down non-combat options for all the classes. If every class is getting additional skill proficiencies and bonuses, skills become more and more trivial.
Also interesting that the discussion turned to issues with the rogue. Historically the rogue was my favorite class; I enjoyed being the skill monkey. But I'm not as enthused with the 5E rogue. The rogue essentially has become the mobile striker. At best, they share the skill monkey spotlight with other classes. At worst, the rogue has been significantly watered down and lost a good chunk of its identity.
Maybe this speaks to a larger issue with 5E. The relative simplicity is a huge factor in its success no doubt. But with that simplicity, variation between the classes and options were sacrificed.
Yes, that's a strong question to ask. When it comes to creating an alternate fighter class (for the minority who want that) or an add-on to the fighter class (again, for the minority) that mechanically – in the class design itself – enhances the fighter's contribution to non-combat encounters, there are two important questions.
The first is conceptual and a question of identity.
What do you want the fighter to be able to do outside of combat that it's not currently doing at your table? And how does your answer inform the
identity of fighters in your campaign?
The second is a question of working within limits. Given all these limitations,
is there design space in 5e for non-combat abilities for the fighter? And, if so, how would those look?
Let's take a look at an example...
I imagine fighters as being really tough, not just physically, but mentally as well. Now, additional saving throw proficiencies are already covered by the fighter getting more feats and being able to take Resilient. But I'm thinking of a gritty warrior who has seen some horrible stuff and is less prone to running away at the sight of a dragon or losing his mind at some horrific thing. Immunity to fear might be an option... but that is primarily useful in combat and steps on the toes of the Paladin's Aura of Courage. So what about immunity/resistance to madness?
We have a strong concept, but that leads to the question of design space. Is madness an optional rule in 5e or is it hard-coded into core rules of the game? Well, there are planar conditions (e.g. Astral & Pandemonium) that cause madness, some artifacts might cause madness, cackle fever (and the horribly named mad monkey fever in ToA) can cause madness, some spells like
contact other plane and
symbol (and potentially
bestow curse) can cause madness... So it seems like it's a pretty core part of the game, even if it doesn't come up regularly.
Next, we ask: How easy is it to remove madness in 5e? This will help give a picture of which level such a class feature would be balanced at. Short-term or long-term madness can be cured with a 2nd-level
calm emotions / lesser restoration, so a fighter could probably get it pretty early around 3rd level. Indefinite madness, however, requires 5th-level spell
greater restoration (which expends 100 gp of diamond dust). So the game distinguishes madness by severity, meaning this feature would need to omit indefinite madness (which is OK because that seems to be rarer in the rules) or have a delayed feature that kicks in around 9th level.
Now I'd consider whether being immune/resistant to madness is enticing enough for a player to select in lieu of other non-combat abilities. Well, it's a passive feature that doesn't really make for cool spotlight moments. Sure, on the rare occasions madness comes up in the game and the fighter is targeted by that effect, it'll be sweet! But having something
else attached to this hypothetical feature would help make it more appealing
and more consistently applicable.
It would be easy to jump to giving advantage on Constitution checks (which are strangely required
instead of saves for resisting extreme heat, dehydration, and exhaustion), but that might be better reserved for a different non-combat ability. Instead, let's double down on the concept of being
mentally tough.
The Sanity score is optional, so we're not going to touch that as part of this design – though a sidebar mentioning how this feature interacts with a campaign where Sanity score is used would be helpful.
What a resistance to enchantment-type magics used out of combat? Things like
charm person, suggestion, dominate person, the jackalwere's Sleep Gaze, or the succubus' Charm? Maybe if the fighter success his save, he can
pretend to have succumbed such an effect? Ah, but then you're treading on the shared creative space of D&D in which any number of character types might want to try that trick. So then we'd need to hunt for the right language in include a variety of effects that are thematically similar but whose only common ground in the rules is targeting Wisdom saves. Maybe something along the lines of "when you are not in initiative and you fail a Wisdom saving throw, you may choose to succeed instead." Obviously not perfect language and it needs a # uses limit, but moving in a good direction.
Now we need to consider whether immunity or resistance (or something else) to madness is the better option. My concern here is if we go with immunity to short-term madness, then a spellcasting PC making heavy use of
contact other plane could multiclass into fighter just for this non-combat ability and circumvent the risk posed by
contact other plane. So either advantage on saves, a way to delay the onset of madness, or some unified mechanic that covers all of the above.
Wrapping it all together, I have two options to choose from...
Hardened Mind (#1). You are immune to long-term madness. When you are not in initiative and you fail a Wisdom saving throw, you may choose to succeed instead. You may use this ability a number of times per day equal to your proficiency bonus.
Hardened Mind (#2). You are immune to long-term madness. When you are not in initiative and you fail a Wisdom saving throw, you may choose to delay the effect of the failed save until you fall unconscious or one minute passes. You must take a short or long rest before using this ability again.
I wanted to write this out long form to demonstrate that, yes, there is design space, but due to the design limitations it is not at all an easy process. And, honestly, I'm not really happy with the
"when you are not in initiative" clause.