  We consider effective Lagrangians which, after electroweak- and
family-symmetry breaking, yield fermionic mass matrices and/or other flavoured
couplings exhibiting residual family symmetries (RFS). Thinking from the bottom
up, these RFS intimately link ultraviolet (UV) Beyond-the-Standard Model (BSM)
physics to infrared flavour phenomenology without direct reference to any
(potentially unfalsifiable) UV dynamics. While this discussion is typically
performed at the level of RFS group generators and the UV flavour groups they
can close, we now also focus on the RFS-implied shape of the low-energy
mass/coupling matrices. We then show how this information can be used to
algorithmically guide the reconstruction of an effective Lagrangian, thereby
forming top-down models realizing the typical bottom-up phenomenological
conclusions. As a first application we take results from scans of finite groups
capable of controlling (through their RFS) CKM or PMNS mixing within the SM
alone. We then extend this to recently studied scenarios where RFS also control
special patterns of leptoquark couplings, thus providing proof-in-principle
completions for such `Simplified Models of Flavourful Leptoquarks.'
