〈かき／掻き／搔き〉〈混／交／雑／ま〉ぜる

Google N-gram Corpus Counts
╭─ーーーーー─┬─────────┬───────╮
│ かき混ぜる │ 114,842 │ 84.5% │ 
│ 掻き混ぜる │   4,492 │  3.3% │
│ 掻き雑ぜる │      44 │  0.0% │ - rK (雑 in daijr/s, koj, iwakoku)
│ 掻き交ぜる │     129 │  0.1% │ - sK (交 in meikyo, smk)
│ 掻きまぜる │     103 │  0.1% │ - sK
│ かき交ぜる │      30 │  0.0% │ - sK
│ 搔き混ぜる │       0 │  0.0% │ - [oK] to [sK]
│ 搔き交ぜる │       0 │  0.0% │ - [oK] to [sK]
│ 搔き雑ぜる │       0 │  0.0% │ - [oK] to [sK]
│ 搔きまぜる │       0 │  0.0% │ - [oK] to [sK]
│ かき雑ぜる │       0 │  0.0% │
│ かきまぜる │  16,255 │ 12.0% │
╰─ーーーーー─┴─────────┴───────╯

@@ -11 +11,2 @@
-<keb>掻き交ぜる</keb>
+<keb>掻き雑ぜる</keb>
+<ke_inf>&rK;</ke_inf>
@@ -14 +15,2 @@
-<keb>掻き雑ぜる</keb>
+<keb>掻き交ぜる</keb>
+<ke_inf>&sK;</ke_inf>
@@ -17,0 +20 @@
+<ke_inf>&sK;</ke_inf>
@@ -20,0 +24 @@
+<ke_inf>&sK;</ke_inf>
@@ -24 +28 @@
-<ke_inf>&oK;</ke_inf>
+<ke_inf>&sK;</ke_inf>
@@ -28 +32 @@
-<ke_inf>&oK;</ke_inf>
+<ke_inf>&sK;</ke_inf>
@@ -32 +36 @@
-<ke_inf>&oK;</ke_inf>
+<ke_inf>&sK;</ke_inf>
@@ -36 +40 @@
-<ke_inf>&oK;</ke_inf>
+<ke_inf>&sK;</ke_inf>

Thanks for the technical info about this kanji. Helpful to know.
I don't object to including 搔 on this entry (and others). I just felt we didn't need a corresponding 搔 form for every existing 掻 form, and that the (kokugo) headword forms were sufficient (which is what I meant when I said "base forms"). 
I didn't actually mean to drop 掻き雑ぜる. And I'll add 搔きまぜる back in because Tyler said he encountered it.
I don't think we need 掻交ぜる, 掻混ぜる, etc., which are all extremely obscure. There are six forms if we include every variant. According to daij and koj, the き isn't optional.

@@ -13,0 +14,3 @@
+<keb>掻き雑ぜる</keb>
+</k_ele>
+<k_ele>
@@ -17,3 +19,0 @@
-<keb>掻き雑ぜる</keb>
-</k_ele>
-<k_ele>
@@ -21,3 +20,0 @@
-</k_ele>
-<k_ele>
-<keb>掻交ぜる</keb>
@@ -32,0 +30,8 @@
+<k_ele>
+<keb>搔き雑ぜる</keb>
+<ke_inf>&oK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>搔きまぜる</keb>
+<ke_inf>&oK;</ke_inf>
+</k_ele>
@@ -37,0 +43 @@
+<pos>&vt;</pos>

Comments from a fork by Tyler:
Apologies, yes I went overboard on this one. It was the first one I did

For each ref, I'd like at least one of their headwords to be included, so they can be found in a cross search. Ideally 
all headwords, since very often some of the forms are missed when scraping dictionary data for external software

搔きまぜる - added this because I actually found it while reading. I guess it's not super necessary though

搔き雑ぜる - added this because it is a headword in 大辞林 (かき ま・ぜる [4][0]【▼搔き混ぜる・▼搔き▽雑ぜる】)
Ideally should be included, but since 搔き混ぜる is here that is enough to pull up the entry

搔混ぜる/搔雑ぜる - headwords in 岩波 (かきま‐ぜる【搔（き）混ぜる・搔（き）雑ぜる】)
Added them to be safe, but yeah if 搔き混ぜる or 搔き雑ぜる are here then that is enough to pull up the entry

The 掻/搔 situation is a result of a process that's been going on in kanji circles for some years. Years ago the JSC people locked in on the simplified 掻 for what became JIS X 0208, then put 搔 into a supplementary standard - JIS X 0212 (which meant no-one used it because Microsoft didn't support it.) Then 搔 was put into Unicode and into JIS X 0213 (an extension of JIS X 0208). Its sort-of legitimization meant that the electronic versions of the kokugos could start including it, which they are now doing, e.g. the 6th edition of 広辞苑.
搔 doesn't show up much in the n-grams because they are derived from oldish data. I expect more contemporary text to show increased use of kanji like 搔.
I think there's no harm in including these forms if they are in kokugos, and I think Tyler has been sticking to that. If terms using them start showing up then people should be able to find them here without having to navigate through base forms. I also think the "oK" is appropriate, at least at this stage.