There are a few ways to get to 4* equipment. One is the standard gear that Kozuma sells, which is easy except for mats. Basil does sell 4* recipes in the Teir 2 terminal, just not every time. It's hard to get exactly what you want from basil. Or you can buy the recipes from people who have found what you want while on their runs. Sure there might be a 1-3k markup on prices, but you don't have to spend 20 T2 runs hunting down each recipe.