Generally speaking, it can work. Practically speaking, it may not.
Depending on the composition of the feed, acidity, base metals in the juice, other elements in... What is the concentration of respective PGMs etc.
PGM chemistry is complicated, and this is the most simplified sequence of how to roughly separate these metals. You will never obtain pure PGM salts/PGMs by one step simple precipitation. You would need to re-refine them once again. Also, if your solutions wouldn´t be concentrated enough, precipitations will be inherently inefficient (like NH4Cl Pt drop, or Cl2 gassing the Pd for example). More "complete" precipitation is, more drag of other PGMs occurs.
This would make many mixed fractions which are contamined with other PGMs, and whole reclamation of values would be much more tricky in the end.
This is why this pathway is not generally used anymore by large scale refineries (maybe russians are still using it, as it is the cheapest process and neglection of worker safety is ongoing issue there) - it is inefficient and tedious, lots of manipulations with hazardous and toxic substances, dusting, liquid waste that need to be stripped from values and then these need to be re-refined etc...
Trust me, I tried very hard to make it simpler and more efficient. Some improvements can be made. But overall, if one factor in the cost of your work and time spent, cleaning, reclamation and re-refining, you will came out the same, if you directly sold the alloy to the bigger buyer. Premiums on high purity PGMs can make additional buck, however, if you look to the whole picture and overall process, you would struggle a lot for minimal if any profit.