Absolutely, it is possible to rework and add circuits under leadless devices like BGA's while maintaining the ever critical flatness characteristics required for successful BGA placement.
This is a modification we perform successfully on a regular basis. However I must caution, this is one of the more challenging rework and repair procedures we encounter. This rework can be difficult because it requires demonstrated skill in multiple disciplines.
Some of the more important capabilities required include BGA removal & replacement, X-Ray inspection, proficiency in milling & cutting of PCB's, the ability to add new circuit components like BGA pads, copper tracks, and jumper wires. The technician's focus on precision and quality of workmanship is paramount to successful results. The complexity of this type of rework and repair is directly proportional to BGA site array density.
If you would like to investigate the procedures in more detail, see BGA ECOs - Nifty Solution or Rework Nightmare?, an article found on the Circuit Technology Center web site. This article details step by step procedures required for a rework/repair of this nature.
Performing repairs/rework under surface mount components to resolve ECO issues is far more common than you might think. Although it is a challenging procedure, it can be done reliably and safely by following established proven procedures. Our experience has demonstrated that skill, attention to detail and patience yields robust, reliable results.
If a program's time to market and ultimate success has stalled because prototypes or production modules need rework or repair under a surface mount component go for the rework or repair. There is no better way to salvage your costly investment and keep your program on schedule.