Thanks to your additional info, OP, the question is now answerable.
So, the overall context is:
Person A: "How should/could one eat elegantly while speaking to another?"
Person B: 「[口]{くち}に[運]{はこ}ぶ[量]{りょう}を[少]{すく}なめにするといいと[思]{おも}いますよ。[三回]{さんかい}ぐらい[噛]{か}んで[飲]{の}み[込]{こ}めるぐらいでいいのでは? 」
「~~ぐらいでいいのでは?」 is an expression of suggesting a method for an action. It gives a rough idea of what should suffice in achieving a good result, which should explain why 「ぐらい = "approximately"」 is being used.
「~~でいいのでは?」 = 「~~でいいのではないでしょうか?」 if that helps you understand the phrase better. It is a way of asking the question: "Wouldn't ~~ suffice?", "Wouldn't ~~ be good enough?"
What is the rough idea being suggested? It is "bringing a somewhat small amount of food into your mouth at a time so that one could swallow it only after chewing it about 3 times".
To say "one could swallow", it uses the potential form 「飲み込める」.