This approach doesn't quite seem to match up with Scripture. Take look at 1 Cor. 12, from which verses 12, 13, and 14 contradict your hypothesis:
12 For as the body is one, and hath many members, and all the members of that one body, being many, are one body: so also is Christ.
13 For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit.
14 For the body is not one member, but many.
The whole chapter follows in the same vein, and quite firmly.
If this doesn't make sense to you, there's not much value in further debating the point of trying to practice the rite of communion apart from the other communicants, is there?
The whole chapter follows in the same vein, and quite firmly.