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If you're trying a single layer, you can argue whether or not the chip will be stable without a ground plane.? However, you may find the layout very difficult (if not impossible) to do.? Of particular difficulty may be the track width when running traces between pads. ? I've done toner transfer with 0.5 mm TQFP packages, and making the pin pads was difficult.

On a double layer, you can't put vias inside the chip, unless you want a pad to be a via? or you can do plated through holes, you may be able to connect only on the top layer.? Again, depends on the complexity of the chip and how fine a trace you can do.? Remember that the standard via is stitched through or an eyelet.? Actual plated through holes are complex to do.

Four layer (and above) boards seem to be very rarely made at home.? The problem is the plated through hole and that you are going to likely need to do photoresist to get the right track size and precision, let alone layer registration and bonding.?

If you can solve these problems (and if they are problems to you), you might be able to make the 4 layer boards you need.? Some BGA chips recommend up to 8 layers.

Generally, though, you may find the production process more complicated than you want to handle, and may need to have the boards made by a professional board house.

Harvey