Yes, this is possible, though the details will be a bit complex. The relationship on which you base the conditional value lists can include additional match fields where you specify additional criteria.
You could also construct a calculation field that uses ExecuteSQL to return a list of ID's and use this as a match field.
And an "exclusion list" can be used to produce a dwindling value lists were previously selected players are automatically omitted by producing a list of all selected player ID's that have been selected and then using them with the not equals operator so that your relation matches to those records with and ID that is NOT in the list.
Such an exclusion list is implemented in this demo file: https://www.dropbox.com/s/oyir7cs0yxmbn6i/ManyToManywDemoWExtras.fp7 to keep from assigning the same contact a second time to a given event. If you are using FileMaker 12, open this file from the File menu to get a copy converted to the .fmp12 file format.
Thanks! I was able to understand the decreasing value list from your example file. I didn't understand how to do a conditional list using certain match criteria that I can select, like limiting the value list to kids in grade 3 & 4, for example.
I have a feeling it's a little too complex for what I can do.
Setting up and using a relationship with more than one pair of match fields isn't terribly difficult.
I can probably walk you through such a process but I'd need a much clearer picture of exactly what you have designed in your database and exactly how you need this to work for you.