PSLV-C37 launched 88 identical satellites into a sun-synchronous orbit. These satellites were for an imaging company called "Planet Labs". Technically the only ones that were identical were the CubeSats (Which were named Doves) but they were launching 4 other types of satellites from this launch too.
The rocket launched Cartosat-2D, a few other satellites and 88 nanosatellites: two from
India, one each from Kazakhstan, Israel, the Netherlands, Switzerland,
and the United Arab Emirates, along with 88 from the United States of
America – 88 Dove satellites and 8 LEMUR satellites.1 The three
Indian satellites launched were Cartosat-2D, INS-1A, and INS-1B.
Arrangements for the launch of the 104 satellites were made between
ISRO's commercial arm Antrix Corporation Limited, under the auspices
of the Indian Government's Department of Space, and the international
In addition to this, it mentions that Planet Labs has 143 total Doves in operation.
Among the 96 satellites belonging to US companies, 88 CubeSats were
owned by Planet Labs, a private Earth imaging company based in San
Francisco, California.2 Weighing roughly 5 kilograms (11 lb) each,
the satellites separated from the rocket in different directions to
avoid collision. With the launch of PSLV-C37, Planet Labs
increased its fleet of satellites to 143, which is the largest private
satellite fleet in operation.
Some more specific information on the Dove 3u cubesat can be found here. Most notably, the following was mentioned in the list of things about it:
Dove satellite constellation holds the world record of the most
satellites launched at once from one rocket and will collect imagery
up to 2 million km² per day. The Dove satellite constellation is a
fleet of nanosatellites deployed from the International Space Station
to take images of Earth. The satellite constellation is operated by
Planet Labs Inc., 88 nanosatellites called Doves weighing only 11
pounds each, provides 3 meter multispectral image resolution for a
variety of mapping applications including several humanitarian and
environmental applications, from monitoring deforestation and
urbanization to improving natural disaster relief and agricultural
yields around the world.
Deployed image of one:
A bunch of them sitting in their stowed state:
So it would seem the answer for max number is 88 and will not be affected by Wednesday.
(Unless someone else finds a different example).