Does anyone have any suggestions for being able to have our front door's doorbell button operate 4 doorbells within the home (one in garage, one in shop and 2 in our 3 story home)? Maybe a particular brand that may allow this setup?

I was hoping there was some way to do this maybe with a higher voltage/wattage transformer (e.g. 16v/30watt), but I'm still not sure if this is enough power. If not, is it at all possible to use multiple transformers to power 4 doorbells connected to a single doorbell button (e.g. maybe with 1 doorbell button connected to 2 transformers where each transformer would be connected to 2 doorbells)?

It seems to me that much larger homes must have similar needs, and I'm wondering how they are addressed. Thanks in advance for all insight and suggestions!

Use the one dorbell button to energize a suitable relay. Use the relay contacts to trigger the separate doorbells.

Selection of the relay, the relay power supply, the interconnecting wires for all of the doorbells, and the proper installation will be left as an exercise for the user.

A couple of minutes on 'ebay' USA found several wireless units with pairs of chimes. At least one advertiser had tunable receivers, so in theory you could fit dozens, by harmonising the codes. The cost would be less than the bell-wire and staples, and you could have multiple pushes too.

These days I am sure you can find solid state chimes that don't draw any significant amount of power at all.

Just purchase 4 wireless units; tune to same DIP switch setting, and hang them where you will.

in theory, if all the chimes are the same voltage and the transformer was of sufficent size, one button could run the whole show. It would required a bit of simple engineering know how. Giving your background, I'd look into a wireless system that will meet your needs like range of the transmitter