Is it possible to level grind in Normal Mode?

Once you're through the first few weeks, you'll start getting an option for which action to take every Saturday. Your options will be:

• Explore Monastery
• Hold Seminar
• Battle
• Rest.

Battle will allow you to battle bandits. You'll have a limited number of "Battle Points" to use depending on your professor level. You can use these to fight battles related to quests you've picked up in the Monastery, fight the default bandit battle every week or once you're far enough, participate in

paralogues.

In addition, in Normal Mode, there is always a free battle. Though the enemies will be a couple levels lower than the "paid" battles, you are free to replay these as many times as you'd like with no cost.

Note however, that to learn a new Class/have support conversations/etc., you'll need to be at the Monastery. So you won't be able to do any of these in between battles (until you end the Saturday and go back).

For more on reasons not to simply do this every time, see Is there a reason not to battle every time?

Although I am not that much further than you are, I am quite certain in saying that there are only limited options of gaining levels.

Every Sunday is your day off. You can usually explore the Monastery to do side activities. Some Sundays offer a battle option. What you can do on these days, is either go battle (thus grind levels), or explore the Monastery as usual, effectively skipping that opportunity to battle.

So, even though grinding opportunities are limited, keep in mind that most gains will come from actually lecturing your students in class. That's where they'll get their new arts, classes and skill levels.

In my own experience, it hasn't really been necessary to grind extra levels. At least, on normal. I can't speak for Hard (yet).