to build on what is already standing: to add further construction to a foundation that has already been laid.
This is the ordinary Greek verb for building (οἰκοδομέω) with the word for "on" fastened to the front, and that small addition changes what the verb claims. It never describes starting from nothing. It assumes that something already stands, that someone else may well have put it there, and that the new work goes on top of it. In every New Testament use the thing already standing is Christ or the message about him, and the new work is people.
Paul uses it for the builders. He laid a foundation in Corinth and other people are now building on it, so the live question is no longer what the foundation is but what the builders are using: gold and silver, or wood and straw. The verb throws all the weight onto the second stage of the job, the stage that will be inspected.
Elsewhere the same verb turns the people into the building rather than the builders:
- believers in Ephesus were set in place on the foundation of the apostles and prophets
- a church in Colossae is being built up in Christ, the way a plant is rooted in soil
- Jude's readers are told to build themselves up on the faith they already hold
In each case the base is not up for discussion. It is already laid, and the only open question is what rises on it.