Interactions in data do provide a more refined adjustment in multiple regression models, though they can lead to parameters which are very difficult to interpret.
I can't say I would recommend using K-means clustering in general unless it was part of a prespecified analysis plan. It's a supervised learning procedure, so it would considerably change the scope and objective of an analysis if applied haphazardly. For something like a mediation analysis where you're interested in latent classes and their relationship with some continuous outcome, this could provide an alternative to multiple adjustment, though I think structural equation modeling would be a superior approach to account for exogenous factors when a "latent state" is an exposure of interest.
In terms of refined adjustment in univariate models or models without interaction, I think the use of splines is worth being knowledgable about. There are many books which cover their use in regression modeling. The number of knots and polynomial degree of splines allow one to control the extent of stratification for factors. I use them almost exclusively in the analysis of ordinal exposure data, since the most sophisticated splines provide adjustment which is equivalent to categorical adjustment and the simplest, linear regression with grouped linear exposure.