Disclaimer: I don't bodybuild and have not tried these.
Boring But Big
The 5/3/1 variant called Boring But Big gets good press. The idea is to do 5 sets of 10 on one major lift each day, then finish the workout with assistance lifts.
Kilgore/Hartman/Lascek's Novice Mass-Gain
Dr. Lon Kilgore (co-author of Starting Strength), Dr. Michael Hartman, and Justin Lascek of 70s Big present a novice mass-gain progression in their book FIT. It recommends 3 sets of 10 on multiple versions of the major lifts as well as a small number of bodybuilding-specific exercises. The authors are well-respected in the S&C community, so I give this program weight.
- Monday: squat, calf raise, overhead press, lat pulldown, shrugs
- Wednesday: bench press, rows, dips, deadlift, weighted crunch
- Friday: front squat, back extension, curls, french press, chin-ups
The exercises in italics alternate between barbell and dumbbell versions each week. Dips and chin-ups are done to failure if one cannot get 10 full reps, and use added weight if one can do more than 10 in a set. Deadlifts only get 1 set, not 3, at the heaviest weight.
GreySkull Linear Progression
You could also look into GreySkull LP: a novice progression, similar to Starting Strength but with more of a focus on upper-body mass gain and aesthetics.