Clojure: Get All Nested Map Values (N levels deep)

I recently needed to pull all the values from a nested map. The map I was working with was designed to give easy access to data like so (formatted):

user=>
(def my-data {"Jay" 
                {"clojure" 
                  {:name "Jay", :language "clojure", :enjoys true}, 
                 "ruby" 
                  {:name "Jay", :language "ruby", :enjoys true}} 
              "Jon" 
                {"java" 
                  {:name "Jon", :language "java", :enjoys true}}} )
#'user/my-data
user=> (get-in my-data ["Jon" "java"])                                                                                                             
 {:name "Jon", :language "java", :enjoys true}            
user=> (get-in my-data ["Jay" "ruby"])                                                                                                             
 {:name "Jay", :language "ruby", :enjoys true} 

This worked for all of the ways the data was accessed, until someone asked for a list of all people and all languages.

I needed a function that grabbed all the values nested to a point in the map (grabbing only the values instead of the deepest map wouldn't have provided valuable information). I created the following function that should grab all the values up to the nesting level specified.

(defn nth-vals* [a i m]
  (if (and (map? m) (> i 0))
    (reduce into a (map (fn [v] (nth-vals* a (dec i) v)) (vals m)))
    (conj a m)))

(defn nth-vals [i m]
  (if (nil? m)
    {}
    (nth-vals* [] i m)))

The nth-vals function can be used as the following example shows. (assuming the same map for my-data) (formatted)

user=> (nth-vals 2 my-data)
[{:name "Jay", :language "clojure", :enjoys true} 
 {:name "Jay", :language "ruby", :enjoys true}
 {:name "Jon", :language "java", :enjoys true}]

For reference, here's what's returned if we reduce the map all the way to it's values.

user=> (nth-vals 3 my-data)
["Jay" "clojure" true "Jay" "ruby" true "Jon" "java" true]

That list of values may be helpful for someone else, but it wouldn't have solved our current problem.

And, if you're interested, here's what's returned if you ask for 1 level deep of values. (formatted, again)

user=> (nth-vals 1 my-data)
[{"clojure" {:name "Jay", :language "clojure", :enjoys true}, 
  "ruby" {:name "Jay", :language "ruby", :enjoys true}} 
 {"java" {:name "Jon", :language "java", :enjoys true}}]

I wouldn't at all be surprised if something like this already exists in Clojure core, but I haven't found it yet.