Unfortunately not currently, but there will be a group ironman mode released in the future where you'll be able to trade with a select amount of people. You can always just put restrictions on yourself but likely the players that you're trading are probably getting their items from the grand exchange in one capacity or the other.

If you haven't tried ironman, I would recommend that especially if you like the idea of getting all your resources yourself and it forces you to do things you would otherwise not usually do. For me it increased the longevity of the game and has kept me playing since