particle が - Use of が in article about Midsummer Day of the Ox and selling eel

I was reading over this article about Midsummer Day of the Ox and selling eel. I'm wondering about the use of が in this sentence

この会社は今年、牛肉のステーキや、ビタミンが多いしじみなども売ることにしました

Roughly: This year the company decided on selling things like beef steak, also many items like basket clams with added vitamins

Why is the が not a で? A part of me reads this as: Vitamins have many basket clams. Which definitely does not make sense

Answer

ビタミンが多いしじみ

The problem is that you are not correctly parsing this phrase.

× many items like basket clams with added vitamins
× vitamins have many basket clams
○ vitamin-rich basket clams

Why is that?

1. 
   

   多い does not substitute "many"
   It's often said Japanese 多い means "many", but it's not true grammar-wise. The correct statement is 「Xが多い」 = "there are many X", that means 多い's lexical meaning, if I'm forced to put it in English, is "a large amount of X exists". And vice versa for 少ない.

   
   


2. 
   

   多い cannot modify しじみ alone
   Due to the aforementioned semantic feature, 多い is not able to move before the noun, as Japanese adjective attribution is actually forming relative clauses. Consider, how could you form a relative clause headed by "people" from "a large amount of people exists"? For this reason, 多いX which is transformed from Xが多い is almost nonsense. Even when you apparently see such construction, it's usually some implicit subject (nominative) hidden.

   
   

   
   

   多い時期は1日1000人 = (観光客が)多い時期は1日1000人 1000 people a day during the season when there are many (visitors) [= high season]

   
   

   多い日も安心 = (経血が)多い日も安心 no worry even on a day where there are much (flow) [sanitary pad ad cliche]

   
   
   

   
   

   The situation is quite contrastive to English many, which cannot stand as predicate i.e. "many people" → *"the people are many".

   
   


3. 
   

   ビタミンが多い modifies しじみ
   Thus you can only interpret the clause ビタミンが多い ("there is much vitamin" or "vitamin is abundant") modifying しじみ. Japanese relative clauses allows any kind of relations between the head noun and the clause, thus you can understand it virtually as "basket clams in which vitamin is abundant".

   
   

   More grammatically correctly, the original sentence before relativization was a topic-comment structure that accepts a complete sentence in the place where English grammar only expect a predicate. This type of construction typically describes such content you use possessive expressions to convey in English.

   
   

   
   

   しじみはビタミンが多い
   As for basket clams, there is much vitamin or basket clams have much vitamin