DateTimeFormatter Accepting Multiple Dates and Converting to One (java.time library)

Question

I am trying to write a DateTimeFormatter that will allow me to take in multiple different String formats, and then convert the String formats to a specific type. Due to the scope of the project and the code that already exists, I cannot use a different type of formatter.

E.g., I want to accept MM/dd/yyyy as well as yyyy-MM-dd'T'HH:mm:ss but then when I print I only want to print to MM/dd/yyyy format and have it in the format when I call LocalDate.format(formatter);

Could someone suggest ideas on how to do this with the java.time.format.*;

Here is how I could do it in org.joda:

// MM/dd/yyyy format
DateTimeFormatter monthDayYear = DateTimeFormat.forPattern("MM/dd/yyyy");
// array of parsers, with all possible input patterns
DateTimeParser[] parsers = {
        // parser for MM/dd/yyyy format
        monthDayYear.getParser(),
        // parser for yyyy-MM-dd'T'HH:mm:ss format
        DateTimeFormat.forPattern("yyyy-MM-dd'T'HH:mm:ss").getParser()
};
DateTimeFormatter parser = new DateTimeFormatterBuilder()
    // use the monthDayYear formatter for output (monthDayYear.getPrinter())
    // and parsers array for input (parsers)
    .append(monthDayYear.getPrinter(), parsers)
    // create formatter (using UTC to avoid DST problems)
    .toFormatter()
    .withZone(DateTimeZone.UTC);

I have not found a good/working example of this online.