Underdeep job advancement after max stage is automatic: once both jobs in a stage sit at level 10 and the Training counter reads 2/2, your character moves on to the next stage tab. There are twelve stages from Stage 0 to Stage 11, two jobs in each, so 24 job slots in total - and after the last stage, job points are no longer where your growth comes from.
Underdeep job advancement after max stage: what happens
The Job panel shows a tab per stage from Stage 0 through Stage 11. Each stage holds exactly two jobs, and the Training counter shows 2/2 while both of that stage's jobs are being trained. Every individual job has its own level displayed as Lv.X / 10, so a job caps at level 10. Each job is levelled with its own experience, and any job can be reset from the same panel, which means a bad early choice is not permanent.
The eight jobs of the first stage
| Job | Stats it raises |
|---|---|
| Adventurer | DEX / HP |
| Courier | POW / TGH |
| Trader | INT / NEG |
| Seeker | SPI / CHA |
| Artisan | DEX / SEN |
| Farmer | TGH / HP |
| Fighter | POW / SPD |
| Thief | SPD / DEX |
Four of these pairs push numbers that fight for you: Adventurer, Farmer, Artisan, Fighter and Thief all feed Dexterity, HP, your attacking stat or the mitigation stats. Trader and Seeker hand out Intelligence, Negotiation and Charisma, which only matter for one-time event checks, so those two pairs are the ones you will mostly leave alone.

Later stages and what to do with them
Every stage is a fresh pair of two stats to push, so the later stages keep feeding the same build. Keep taking HP alongside Dexterity or your attacking stat so a single slot pushes two useful numbers, and use the priority order in the build guide to decide which pair to take when a stage offers more than one useful option.
Jobs never unlock skills
A job awards points into its two stats and gives no new skill, ability or action. All skill content comes from Orbs, so a maxed job stage only makes you stronger in the panel, never richer in the Skill tab. Where those Orbs go is covered in the skills and Orbs guide.