1st step: discuss with the group
If everyone but Player #2 is happy with kill-em-all hack-n-slay, so be it, don't waste your time...
but, if the majority want more plot and more RP, go for it.
2nd step: Small improvements
numerous small improvements can be made. Things like having the bad guys sass the group, using the morale rules (in the DMG), and requiring a statement in character voice to attempt a social roll. (If it's really good, give advantage; if it's absent, disadvantage)...
Give advantage for particularly good (but open ended) descriptions of the attempt...
Exempli Boni: "I wind up, while charging, and whip my warhammer around at him"
Exempli boni: vs an invisible target: "I thrash about with my sword at the rustling of his garments."
Exempli Mali: "I stab him through and through" - bad, because it presumes the hit.
Exempli mali: "I attack" - not descriptive
Exempli Boni: "I attempt to convince the guard to let me through, by talking to him about his mother, the weather, and how mad the boss will be, and disappointed his mother will be, when he realizes I've not been admitted."
3rd step: include explicitly non-combat but mechanically resolved encounters
These are especially good if they are the objective of the mission... for example, "Go convince the hobgoblins to attack Akkad, rather than us Husnak." Sure, the PC's probably could level up for months on a steady diet of "sneak in, kill a few dozen hobgoblins, and escape"... but when there are 10,000 of them camped on the border? Note that Hobgobs DO form real armies, with chains of command and all... so, "Take me to your leader" may require proving that you aren't actually dinner on the hoof... but once you do, it's time to go see the boss.
Why send the PC's instead of the generals? E-X-P-E-N-D-A-B-L-I-T-Y!!!
PC's are a sociodynamic problem for D&D rulers - high level characters have excess wealth, strange ideas, good weapons, good armor, and often, also have personal lines of communication with one or more deities... The local ruler would be just as happy to see them eaten by Hobgoblins as to have then successfully convince the Hobgob general to attack the other way. And more than one group of PC's has committed a Coup d'état and/or revolución de Junta (with peasants and/or enemies). PC-like bands of NPC's immediately raise player red-flags - and would do the same to NPC leaders.