GG5: a three-pronged fork; a trident.
	～の three-forked 《road》; three-pronged; trifurcate(d).
中辞典: a three-pronged fork; a trident; 〈ソケット〉 a three-way socket
	¶三つ叉の角(つの) a three-pronged antler
	･三つ叉の道 a forked road.
三つ又	10719	81.5%
三つ叉	1341	10.2% = most of the JEs
三つまた	673	5.1% - JE examples
三つ股	426	3.2% - kokugos

I think it should stay with the two senses, but clearly the adjectival use dominates.. The  さんさ reading can go.

@@ -14,0 +15 @@
+<ke_inf>&rK;</ke_inf>
@@ -17,0 +19 @@
+<ke_inf>&sK;</ke_inf>
@@ -20,0 +23 @@
+<ke_inf>&sK;</ke_inf>
@@ -27,4 +30 @@
-<pos>&adj-f;</pos>
-<xref type="see" seq="1300460">三叉路・さんさろ</xref>
-<xref type="see" seq="1813990">三叉神経・さんさしんけい</xref>
-<gloss>three-pronged(e.g. spear, fork)</gloss>
+<gloss>three-pronged</gloss>
@@ -32,0 +33,5 @@
+</sense>
+<sense>
+<pos>&n;</pos>
+<gloss>three-pronged fork</gloss>
+<gloss>trident</gloss>

sankoku: 三つ叉
三本に別れている＜こと・もの＞「ーソケットの川筋」

sankoku 三椏 The flower (みつまた)

sankoku　
三叉神経(さんさしんけい), (we have this entry already)
三叉路（さんさろ）:道が三方向に分かれている道路。みつまた  (we have this entry already)

三叉槍
Wikipedia: "三叉の矛" (three-pronged lance/ tri-tipped lance... )
ギリシア神話において、ポセイドーンはギリシアの水源や馬を作り出すのに古代ギリシア語でトリアイナ (τρίαινα) と呼ばれる***三叉の矛****を使用した


https://item.rakuten.co.jp/jism/4537807190192-55-7760-n/?variantId=4537807190192-55-7760-n
In the context of a trident:
「四天王像」から、三つ叉の戟を携え　(the の戟 is required) 

三つ叉	1341	1.5%
三つ又	10719	11.7%
三つまた	673	0.7%
三つ股	426	0.5%

三叉	57409	62.8%
三又	20876	22.8%

but...
三叉路	60330
三叉神経	33944

三又の	3473	34.4%
三叉の	3442	34.1%
三つ又の	2499	24.8%
三つ叉の	358	3.5%
三つ股の	131	1.3%
三つまたの	183	1.8%

三叉の槍	551	45.0%
三つ又の槍	375	30.6%
三又の槍	256	20.9%

三つ股の枝	47	42.3%
三つ又の枝	38	34.2%
三叉の枝	26	23.4%

Magic the Gathering card:  三叉矛 =  みつまたほこ
https://paypayfleamarket.yahoo.co.jp/item/z178717584

The plant(I guess this is different kanji, discussed earlier):
https://japanknowledge.com/introduction/keyword.html?i=1632
ミツマタ
みつまた／三椏
[学]Edgeworthia chrysantha Lindl.
[学]Edgeworthia papyrifera Sieb. et Zucc.

Tyler said, "三つ又 10719 // I found it in this form; did happen to be in the context of a trident".

I have also seen this in the *context* of a trident (something like 三叉の矛, as on wikipedia).

It does not appear that this term would ever be taken to *mean* trident in isolation.  I have proposed two such entries separately: 三叉槍 三叉戟 (compare google image results for either of those, and any kanji entry here).  I have encountered a third , apparently recent coinage, which I am ignoring 三又矛（みつまたほこ）。

Actually, I see no clear support for [1] at all.  both sankoku and daijs give no straight [n] sense for 三つ叉, other than a clothes-drying-related tool, and the plant.

There seem to be some historically "grandfathered" terms with the さんさ reading, all of which we now have in jmdict:
The two spears entries I just added,
trigeminal nerve/neuralgia (三叉神経)
three-way intersection (三叉路)
There is a mountain named 三叉峰　さんしゃみね that we don't have (different reading, しゃ, as well).  

Beyond that, the さんさ reading does not seem to be productive, and doesn't seem to need an entry outside of those terms.  sankoku, for example, gives only 三叉路 and 三叉神経。Otherwise "さんさ" has no dedicated entry.

For new terms, the reading seems to always be みつまた. 
三叉コンセント (three-port outlet) appears to be みつまた, not　さんさ.

Magic The Gathering card game decided to use 三叉矛 , which I would have guessed as さんさほこ, but they furigana as みつまたほこ.

Here's a whimsical illustration of the clothes-drying stick, if interested:
物干し竿と三叉
https://twitter.com/koikawa01/status/1138437149328412672

Added xrefs to warn about the only two notable reading exceptions, which seems more useful than a generic "sometimes read as さんさ". I'm not arguing that this is a good approach in general(not something I would run around trying to do elsewhere), but for this specific case it seems like a clean approach that eliminates a lot of ambiguity.

If insisting on a standalone noun sense, I think it would be
: any object with three forks, prongs, branches, etc....
But "trident" and "three-pronged fork" seem way too specific and would rarely be correct for a random occurrence of 三つ又.　And by relative volume, this is practically never the "subject" of a sentence, which is a final reason I don't think a dedicated [n] entry is needed:
三又が	412
三叉が	196
三つ又が	160
三つ叉が	30
三つまたが	0
三つ股が	0

@@ -18,0 +19,3 @@
+<k_ele>
+<keb>三又</keb>
+</k_ele>
@@ -22,4 +24,0 @@
-<r_ele>
-<reb>さんさ</reb>
-<re_restr>三叉</re_restr>
-</r_ele>
@@ -27,6 +25,0 @@
-<pos>&n;</pos>
-<gloss>three-pronged fork</gloss>
-<gloss>trident</gloss>
-</sense>
-<sense>
-<stagr>みつまた</stagr>
@@ -34,3 +27,6 @@
-<gloss>trifurcate</gloss>
-<gloss>three-pronged</gloss>
-<gloss>three-way (e.g. outlet)</gloss>
+<pos>&adj-f;</pos>
+<xref type="see" seq="1300460">三叉路・さんさろ</xref>
+<xref type="see" seq="1813990">三叉神経・さんさしんけい</xref>
+<gloss>three-pronged(e.g. spear, fork)</gloss>
+<gloss>three-way (e.g. outlet, intersection)</gloss>
+<gloss>trifurcated</gloss>

Quiet. Closing.

Reordered on n-grams (ルミナス has 三つ又, other JEs and kokugos 三つ叉)
Dropped  ミツマタ - confused with 三椏.
I think it works better with the adjectival sense split out.

@@ -5 +5 @@
-<keb>三つまた</keb>
+<keb>三つ又</keb>
@@ -11 +11 @@
-<keb>三つ股</keb>
+<keb>三つまた</keb>
@@ -14 +14 @@
-<keb>三つ又</keb>
+<keb>三つ股</keb>
@@ -26,4 +25,0 @@
-<r_ele>
-<reb>ミツマタ</reb>
-<re_nokanji/>
-</r_ele>
@@ -32 +27,0 @@
-<pos>&adj-no;</pos>
@@ -34,0 +30,7 @@
+</sense>
+<sense>
+<stagr>みつまた</stagr>
+<pos>&adj-no;</pos>
+<gloss>trifurcate</gloss>
+<gloss>three-pronged</gloss>
+<gloss>three-way (e.g. outlet)</gloss>

Google N-gram Corpus Counts
三つ又	10719 // I found it in this form; did happen to be in the context of a trident
三つ叉	1341
三つまた	673
三つ股	426

三叉	57409
三又	20876 // seems to be a name, but if you image search 三又 -三又又三 you do get a lot of valid results

岩波国語辞典
 みつまた
① 【三（つ）又・三叉】３方向に分かれていること。また、川・道などが３本に分かれている所。
② 【三椏】じんちょうげ科の落葉低木。etc plant stuff

* I think the word is more general than this
* I'm only getting images of 三椏 when searching ミツマタ on google images
* not sure how to sort everything due to all the crossover

gonna leave this one to the experts :^)