The quartered arms you blazon are not the "Tower Coat of Arms" as you describe them but are the coat of arms of one particular man. The first quarter is the pronominal coat of (a person named) Tower. The second, third and fourth quarters represent the arms of heraldic heiress's who have been the ancestors of this particular person and have brought into his coat of arms the armorial bearings of other families. I do not have the time to research these arms today but I do not think there is a coat representing Plantagenet.
To this end this quartered coat can not be the generic coat of arms for the family of Tower (indeed there is no such beast) but only of one particular family; the family that has these heiress's in its tree. It is not a case of (as you said in your first post) the Sackvilles (and others) using the arms of Tower but should more accurately be described as a particular family of Tower using the arms of Sackville (and others) by right of marriage to an heraldic heiress or heiresses. You need to find out what heiresses came into the family of this particular Mr. Tower to find out what families the coats you refer to represent.
For an example of quarterings where the represented families are named you could do worse than browse my Cheshire heraldry site - for example the following page; http://cheshire-heraldry.org.uk/visitations1613/CV1613_16.htmlhttp://cheshire-heraldry.org.uk/visitations1613/CV1613_16.html where you will se the arms of Marbury of Marbury [representative arms of the heiresses in brackets] Arms: Quarterly of eight: 1 & 8 Sable, a cross between four pheons Argent [Marbury] 2 Or, on a fess engrailed Azure three garbs of the first [Marbury Ancient] 3 Argent, a lion rampant Gules, collared Or [Redish] 4 Sable, three asses' heads caboshed Argent [ ? ] 5 Vert, a cross patonce Or [Boydell] 6 Argent, on a fess Sable three mullets of the field [Boydell?] 7 Gules [Argent] a castle tripple towered Argent [Gules] [Doncaster]
Crest: On a cap of maintenance Gules, turned up Argent, five bezants, a sarecen's head couped at the neck proper, wreathed round the temples Or and Azure.