I see a lot of different ideas getting mixed up here. Private Masses deserve a seperate thread. In Catholic Canon Law every priest is encouraged to say the Mass daily (aliturgical days excepted) and is seen to have the right to do so, even if there is no pastoral need, However it is expected that he will be assited by one server. "Where two or three are gatehred in my name..."
Votive Masses are also a seperate thread. On a Ferial day the celebrating priest has the right to choose the Mass Propers. For example, he could say a Mas in honor of the Mother of God. That is what a Mass for Chrsitian Unity would fall under.
I would say "in all and for all" is an accurate description of what the Catholic Church teaches. Since it is Christ who offers and is offered the fruits of the Mass are infinite and of course the entire, Church, living and departed, is commerated and benefits at every Mass/Liturgy. However, some are mentioned generally and other specifically. Those mentioned specifically may be mentioned aloud or quitely during the dyptychs or during a litany or in the Byzantine tradition during the Proskomede.
The faithful may also make an offering with a request for a commemoration. Catholic Canon Law forbids a priest from accepting more than one offering per day. The diocesan bishop sets the customary amount of offering but a priest is obviously not deny the request of those to poor to make an offering. It is this rule that seems to have created the idea among the misinformed that a Mass benefits a single person soley because an offering was made. The rule is in place to prevent priests from getting rich by accepting offerings they have no ability or intention of fulfilling. The priest can commemorate as many people as he chooses, but he can only accept one offering and he must commemorate those for whom the offering was made.
