Since you are not allowed to put more than two conditions in one condition group (And | Or) you have to create an extra nested group (MSDN). The expression A AND B AND C
looks like this:
<And>
A
<And>
B
C
</And>
</And>
Your SQL like sample translated to CAML (hopefully with matching XML tags ;) ):
<Where>
<And>
<Or>
<Eq>
<FieldRef Name='FirstName' />
<Value Type='Text'>John</Value>
</Eq>
<Or>
<Eq>
<FieldRef Name='LastName' />
<Value Type='Text'>John</Value>
</Eq>
<Eq>
<FieldRef Name='Profile' />
<Value Type='Text'>John</Value>
</Eq>
</Or>
</Or>
<And>
<Or>
<Eq>
<FieldRef Name='FirstName' />
<Value Type='Text'>Doe</Value>
</Eq>
<Or>
<Eq>
<FieldRef Name='LastName' />
<Value Type='Text'>Doe</Value>
</Eq>
<Eq>
<FieldRef Name='Profile' />
<Value Type='Text'>Doe</Value>
</Eq>
</Or>
</Or>
<Or>
<Eq>
<FieldRef Name='FirstName' />
<Value Type='Text'>123</Value>
</Eq>
<Or>
<Eq>
<FieldRef Name='LastName' />
<Value Type='Text'>123</Value>
</Eq>
<Eq>
<FieldRef Name='Profile' />
<Value Type='Text'>123</Value>
</Eq>
</Or>
</Or>
</And>
</And>
</Where>