Building large S-Boxes from smaller ones I would like to make an exhaustive list of all relevant techniques that have been studied in order to build a large S-Box from smaller ones.
As far as I known, three structures are usually preferred:


The Lai-Massey construction (used to design the IDEA block cipher)
Feistel networks (used to build $2n$-bit permutations from $n$-bit permutations)
MISTY networks (initially combines an $(n-1)$-bit S-Box with an $(n+1)$-bit one in this document)


Notably, this publication analyzes pros and cons of using either Feistel or MISTY networks to build 8-bit S-Boxes.

Are there any other relevant techniques to design large S-Boxes from smaller ones?
Yes , there are others such as SPN (CLEFIA , Khazad Middori-128 ,etc) 

in addition to xor-based Feistel  structure , the Kuznyechik is based on product-based Feistel  structure.

I suggest to read this thesis (it summaries all) : CRYPTANALYSIS, REVERSE-ENGINEERING AND DESIGN OF SYMMETRIC CRYPTOGRAPHIC ALGORITHMS