It is definitely possible if you have some electrical splicing and insulating skills.
 
The fans don't have to use any power from the card at all.  All the fans need is the PWM signal from the card to each fan (in blue below), and 1 (and only 1!) fan needs to send tachometer signal (in green below) back to the card.  The fans' 12v power and ground (in yellow and black below) can connect straight to a 4-pin molex connector for their power source.  Make sure that you don't accidentally send more than 1 fans' tachometer signal back to the card, otherwise the fan control will be haywire due to clashing signals.  If you use off-the-shelf fan splitters, you might have to cut the tachometer signal wire on one of the splitters in order to prevent multiple tachometer feedback signals from reaching the card.
 
Here is a sketch I posted in this forum some time in the past.  You can use your imagination about how to add 2 more fans to that schematic:

 
 
Edit, fine, no imagination needed...
 

 

This is what I use:
https://www.amazon.com/Cable-Matters-2-Pack-3-Fan-Splitter/dp/B01DV1Z0WC
 
...Or at least something identical in appearance.  I don't remember if it was the exact same brand or model.
 
With those 2, you can control up to 5 fans, and not worry about the tach feedback issue as long as the 2nd daisy-chained one is plugged into the first one which has the green tach wire.
 

 
As long as only one fan total is connected to a green wire, the fan tachometer thing is taken care of.  I hope that makes sense.
 
You can probably find a version with sleeved wires and black connectors if you don't like the appearance.  I use my splitters behind my motherboard tray, so I don't have to worry about the appearance.

Running 4 nf-a12x25s in push/pull on my hybrid kit using 2 y-splitters. Works totally fine. I believe each fan is 0.15 amps

I wouldn't recommend a splitter which doesn't have a power connector.  I mean, you might not fry the card's fan header, but it is a small gamble.  But there is a bigger reason not to use the card's fan header for the fans' power: power limit.  These cards are very power limited and any power the fans use will reduce the power available to the GPU and affects how high the card will boost.
 
I would recommend this:
The one I posted above, or this slightly prettier version: https://www.coolerguys.com/products/evercool-fan-cable-5-pwm-fans-cb-ec-df001
 
Not this:
https://www.amazon.com/Splitter-TeamProfitcom-Computer-Extension-Converter/dp/B07TRV6XZX
 
Do as you wish.  Both methods will work.  One method is a little less messier than the other method, but the messier method is safer and can provide better overall results.