We describe the process of stacking radio interferometry visibilities to form a deep composite image and its application to the observation of transient phenomena . We apply “ visibility stacking ” to 46 archival Very Large Array observations of nearby type Ia supernovae ( SNeIa ) . This new approach provides an upper limit on the SNIa ensemble peak radio luminosity of 1.2 \times 10 ^ { 25 } \mathrm { erg } \mathrm { s } ^ { -1 } \mathrm { Hz } ^ { -1 } at 5 GHz , which is 5–10 times lower than previously measured . This luminosity implies an upper limit on the average companion stellar wind mass loss rate of 1.3 \times 10 ^ { -7 } \mathrm { M } _ { \sun } \mathrm { yr } ^ { -1 } . This mass loss rate is consistent with the double degenerate scenario for SNeIa and rules out intermediate and high mass companions in the single degenerate scenario . In the era of time domain astronomy , techniques such as visibility stacking will be important in extracting the maximum amount of information from observations of populations of short lived events .