Yes—this is essentially a focus-stacking workflow, and software can automate much of it if the camera position stays fixed. The general process is:

1. Take multiple photos with different focus points.
2. Import them as layers in one document.
3. Auto-align the layers.
4. Auto-blend the layers so the sharp areas from each frame are combined.
5. Fine-tune masks, tone, and color if needed.

Photoshop supports this approach with Auto-Align Layers and Auto-Blend Layers. In practice, it works best when nothing moves between frames. For a portrait, movement from the subject, hair, clothing, or changing light can make the blend less perfect, so some manual cleanup may still be needed.

If your subject fully leaves the frame for the background shot, the software may not always produce the exact result you want automatically, but the aligned-layer and blending approach is the standard starting point.