Is there any way to upgrade the hydraulic pump on a Yanmar SA424? Seems to very tough to operate 2 functions on backhoe.
I'm going to assume you have tried all the simple things - like making sure that the backhoe return line is large enough that it is not restricting flow, and checking that running at a faster RPM does clearly supply more oil to the BH functions than running at idle.
Most small tractors don't have much hydraulic flow - and what they do have is reserved for the power steering and 3pt. There are ways to mess with that and steal some flow. I don't recommend it, but we can talk about it if you want to learn some hydraulics.
The tradtional fix for low tractor flow to a backhoe attachment is taken care of when the backhoe attachment is ordered. The buyer checks the specs, and if flow is minimal then instead of adding hydraulic remotes to the tractor, the backhoe is ordered with the optional integral hydraulic system driven by the tractor PTO. At the time of purchase that adds a few thousand dollars to the price of the hoe, and there is plenty of flow for anything.
Take a look at some univerals backhoe attachments and you will see that many of them can be ordered with or without a PTO-driven pump and that the price is often a thousand to two thousand dollars higher for one with a PTO pump and reservoir.
If you want to do some fabrication, you can certainly add that functionaity to your existing backhoe and it will really make it jump. That would mean addng a pump, a reservoir, and some plumbing. There are 3pt driven hydraulic kits on the market that will give you the idea. Most are mounted under the backhoe seat. That way your backhoe hydraulics would have more than enough flow and also be completely independent of the tractor hydraulics.
rScotty