Code base is littered with code like this:

BaseRecord record = // some BaseRecord
switch(record.source()) {
    case FOO:
        return process((FooRecord)record);
    case BAR:
        return process((BarRecord)record);
    case QUUX:
        return process((QuuxRecord)record);
    .
    . // ~25 more cases
    .
}

and then

private SomeClass process(BarRecord record) { }
private SomeClass process(FooRecord record) { }
private SomeClass process(QuuxRecord record) { }

It makes me terribly sad. Then, every time a new class is derived from BaseRecord, we have to chase all over our code base updating these case statements and adding new process methods. This kind of logic is repeated everywhere, I think too many to add a method for each and override in the classes. How can I improve this?