Under what conditions can a re-married Catholic couple receive the sacrament of the eucharist? According to familiaris consortio, the only case where a "civilly" re-married Catholic may receive communion, is where they repent and live like brother-sister, so to speak. 

Are there other, perhaps special situations, where such a Catholic may be allowed to receive the Eucharist? Is there some applicable canon law, other papal, or something in the catechism that I may not be aware of?

We are assuming that the re-married catholic had a prior valid marriage in Catholic church that has not yet been declared null, and that the second marriage is a civil marriage only.
Are there other, perhaps special situation, where such a Catholic - divorced and remarried - may be allowed to receive the Eucharist?

No there aren't
Unless a declaration of nullity [cf.entire Ch 1 (Art 1-7) Code of Canon Law] is issued on the prior marriage, and the current marriage convalidated.


  a. Epikeia and aequitas canonica exist in the sphere of human and
  purely ecclesiastical norms of great significance, but cannot be
  applied to those norms over which the Church has no discretionary
  authority. The indissoluble nature of marriage is one of these norms
  which goes back to Christ Himself and is thus identified as a norm of
  divine law. The Church cannot sanction pastoral practices - for
  example, sacramental pastoral practices - which contradict the clear
  instruction of the Lord.
  
  In other words, if the prior marriage of two divorced and remarried members of the faithful was valid, under no circumstances can their
  new union be considered lawful and therefore reception of the
  sacraments is intrinsically impossible. The conscience of the
  individual is bound to this norm without exception.2
  
  2 Cf. Angel Rodríguez Luño, L’epicheia nella cura pastorale
  dei fedeli divorziati risposati, ibid., pp. 75-87; Piero Giorgio
  Marcuzzi, S.D.B., Applicazione di "aequitas et epikeia" ai contenuti
  della Lettera della Congregazione per la Dottrina della Fede del 14
  settembre 1994, ibid., pp. 88-98; Gilles Pelland, S.J., La pratica
  della Chiesa antica relativa ai fedeli divorziati risposati, ibid.,
  pp. 99-131.
  
  Source: Objections to the Church's Teaching on the Reception of Holy Communion by Divorced and Remarried Members of the Faithful by Joseph Cardinal Ratzinger | Congregation for the Doctrine for the Faith.




Please see also


  CCC 1665 The remarriage of persons divorced from a living, lawful
  spouse contravenes the plan and law of God as taught by Christ. They
  are not separated from the Church, but they cannot receive Eucharistic
  communion. They will lead Christian lives especially by educating
  their children in the faith.


And

CDF October 22, 2014 response to the Question of a French Priest: "Can a confessor grant absolution to a penitent who, having been religiously married, has contracted a second union following divorce?"



Endnote


OP contained - "civilly" re-married Catholic - wording. If one is re-married, there must have been a prior marriage that ended in a divorce.
A Sacramental marriage is a marriage between two baptized persons. A valid marriage between a Catholic and a non-baptized person is NOT a sacramental marriage.
If a Catholic marries not observing the Church's laws on marriage, that marriage is invalid.




Please see this answer to: Is a Catholic annulment divorce in a Catholic way?