Frits which make rice grain bulbils may be more inclined to make more of these, even breaking the main bulbs down to rice if the conditions are not to their liking. This may be because they are not getting enough water, or are too hot - that may be because they are not deep enough and little frit bulbils, unlike say, narcissus, are not able to pull themselves deeper in such a neat way as the narcissus can. The result is the same though - narcissus working on getting their bulbs deeper will not flower, neither will a frit making masses of rice grains.
If the main bulb of a rice making frit is in good conditions it is able to both renew flowering sizes itself and also make babies.
I think a good feed now with Sulphate of potash - or potassium rich fertiliser as I mentioned before, is the best way forward. When the growth dies down you can lift and split the clump to give the bulbs more room.