A complete protein for humans will be achieved using milk proteins but there is a possibility for combining proteins to achieve same nutrition

complete protein (or whole protein) is a source of protein that contains an adequate proportion of all nine of the essential amino acids necessary for the dietary needs of humans or other animals.[1] Some incomplete protein sources may contain all essential amino acids, but a complete protein contains them in correct proportions for supporting biological functions in the human body.

The following table lists the optimal profile of the essential amino acids, which comprises a complete protein:[2]

Essential Amino Acid mg/g of Protein Rice
Tryptophan 7
Threonine 27
Isoleucine 25
Leucine 55
Lysine 51
Methionine+Cystine 25
Phenylalanine+Tyrosine 47
Valine 32
Histidine 18

Whey protein comes very close as a source of a complete protein. However you do not really need a complete source in one shot. Combining proteins even at diffrenet times of the day can give you all the essentail amino acids. Thus by using other sources you can achieve this.

Rice protein for example contains many of the above but is low in Lysine and Leucine. This is typical of cereals. By using protein from peas and other leguminous sources the complete profile can be achieved if a total plant product is required. Or blending with whey can be an option too.

Of course other parameters such as taste, solubility and price are important.

Protein Digestibility Corrected Amino Acid Score (PDCAAS) is a method of evaluating the protein quality based on both the amino acid requirements of humans and their ability to digest it. Whey and other milk proteins are tops and rice and pulses have lower PDCAAS due to limts of some amino acid. However a combination of two proteins raises the PDCAAS to that of Whey.

It can be seen that it is possible to achieve the effects of whey by combing two or more other proteins  such as rice and pea. The taste and solubility may be another factor in looking for whey substitutes.

The human species is the only mammal that consumes milk products after infancy.

Sources and Acknowledgements to Wikipedia