Your building may not suit a full free-standing timber frame. If it is built into a hillside for example and damp control is going to be an issue, then masonry construction nees to be employed on the lower levels.
Your building can still be given some oak framed character by employing timber where it is really on show, such as in the roof. It is common for us to slot perhaps an oak framed first-floor structure, or just a single 'A'-frame truss into what is basically a block-wall construction.
Oak frame work on stone barn conversions falls under this category.