For the question about eggs: no limit, you can eat as much as your body wants to.
I dont' recommend supplementations because:
1. it is still a way to escape our responsability of 3D beings to eat 2D beings, both animals and plants, and to be grateful to both of them.
2. it's the easy way
3. they are not as good as real nutrients, real proteins and real vitamines you can find in meat
4. they are plenty of bad stuff, titane oxyde (gives cancer) and other artificial chemicals
You want to get protein animals but don't want to help local ethical farmers to maintain their job? I don(t understand this position.
Animals know, deep in them (soul group), that they will end being eaten (like plants ends being eaten by them, and by us). They (animals) will be relieved if we do it with respect, and with gratitude, if we recognize that thanks to their sacrifice we are healthy and joyful to share our barbecue with family and friends on a sunday. And that -very important- in return we give them a happy life (freedom, well nourished i.e. natural grass without pesticides, farmer visiting and talking to them every day, etc...)
I'll love to get a farm and deal with animals that way, but nobody around me is interested. Most people love the "comfort" of their life, love their "clean" job in offices, love the comfort to go and easily buy meats that are already cut and packed, ready to cook.
And if you still want to get animal proteins in your body without having the courage to fullfil your responsability, there are lab grown meat for vegetarians. If you're interested in artificial meat, here is an article on Sally Norton's blog:
sallyknorton.com