replacing transom support plate?

If it is a small outboard you could stand on the skeg temporarily. Not ideal though.

If you mean what I think you mean by transom support plate then you need to do more than just replacing the plate.

As Brett said - post pictures.

 

If I understand you correctly then you tilt the motor all the way down and put a block of wood under the skeg.  Block the wheels of the trailer to keep it from moving and use the tongue jack to lower the transom just enough take the weight off of the through bolts so you can install the new plate. That does not look like a huge motor, so it should be fine. If you are worried about it build a cradle that fits around the cavitation plate and distributes the weight more.

Ducknut may be right though, there could be more damage than just the plate.  It depends on why that plate is damaged to start with. Could be from an impact, over tightening, transom rot etc etc? Take a good hard look, you may find things you don't want to.

Swamp

 

After opening the pic and zooming in to see details,
all I'd do is remove the mount bolt on the unbroken side
and remove the broken plate. Then add an oversized stainless steel  fenderwasher,
new sealant and retighten. The replace the fenderwasher on the other side
with an oversized stainless washer, new sealant and retighten.
I don't think I'd even have to remove the outboard.

:-?