Brew in a bag with a 4 gallon kettle

Ok here's what you want to do.

Do the steep as instructed. When you remove the grains just before 170°F, sqeeze the bag the best you can to get as much wort as possible, silicone bbq mits help. Now at 1.75 gallons after grain absorption

Then top off to your kettle capacity with water, add DME, mix well and continue with boil without a lid on. Now at 4 gallons.

After a 60 min boil you will lose about 1 gallon. Now at 3 gallons. Top off again, now back to 4 gallons and wort has a head start on the chilling. Chill this wort and add to fermentor.

Boil more water and chill to top off your fermentor with. Now at 5 gallons in the fermentor.

This whole process is a partial boil method. Your grains are most likely only crystal malts for color / flavor and don't need a mash, only steeping.

Recipe needs to be designed for a 5 gallon batch though, if it's designed for less you will just get watered down wort and a lower ABV beer.

I am not an expert, but I am also a BIABer and a I work with a small kettle (about 19 liters). So I am always trying to retrieve as much wort as I can with the limitations of my equipment.

Something that I recently learn adapting recipes to my equipment, is that yes is possible to make a more concentrate wort that fits size of my/your kettle, and after that dilute it as required in the fermentor.

However... You must be carefull with two points:

• Obtaining sugar from grains depends on the quantity of water you use in the mash. That means, if you mash with less water than the specified in the recipe you will need more grain to obtain the required quantity. Though this point does not apply to you, as you are only steeping and not mashing ;)
• On the other hand, at the moment of boil, you should be care about the hops additions. As the wort is more concentrated, extraction of oils and AA from hops is not the same, so you must increase hops quantity a bit also in order to retrieve same IBUS as the original recipe

Summary/Conclussion

This is the theory, not sure about the how noticeable will be hop propportions in your case, (also depends on the beer style, though).

In your possition, I will go to boilling 4 gallons as proposed, and I would add a little bit more hops than required.

That a little bit, is a tricky question. Maybe if you provide more info about the recipe and hops additions someone could give you more detail, or you could also try for yourself to calculate it with some software/tool.

I would recomend you reading following thread. It is about a concrete tool BIABacus, but I believe it will help you explaining the dilutions.

How much beer can I get from my kettle?