In other words: Do you have a right to the assistance of counsel if you elect to assume charge of the strategic and tactical control of your own defense in a criminal prosecution and elect to speak for yourself in your own defense?
By "elect to speak for yourself in your own defense", I'm taking that to mean that you will do all the speaking for yourself.
In that case, in england-and-wales you are entitled to the assistance of anyone you like, whether legally qualifed or not. Such a person is known as a McKenzie friend, named after the person who won the right to have one.
They do not have rights of audience however, so if you intended that you would both address the court, then my answer will not be applicable. In some cases, you may have little choice about having a mixed approach e.g in jurisidctions where a litigant-in-person has no right to cross-examine alleged rape victims.
Amendment VI provides that "[i]n all criminal prosecutions, the accused shall enjoy the right ... to have the assistance of counsel for his defense."
Gideon v. Wainwright, 372 U.S. 335 (1963) over ruled Betts v. Brady, 316 U.S. 455 (1942) which held that state courts had to appoint counsel if the defendant showed "special circumstances" requiring representation by counsel which stipulation eerily resembles to the state of the handling of pro se defendant's Sixth Amendment rights to the assistance of counsel.
Right to "advisory" or "standby" counsel; right to assistance (not representation) of counsel
Developments in California reached similar although rather subtly and not concisely expressed conclusions relating to the right to the assistance after a Faretta motion:
[...] United States v. Schmidt (2d Cir. 1997) 105 F.3d 82, 90; United States v. Cochrane (9th Cir. 1993) 985 F.2d 1027, 1029; and United States v. Windsor (7th Cir. 1992) 981 F.2d 943, 946-947 [... each] of these decisions ... left open the possibility that on [certain] facts the federal court might allow a pro se defendant to challenge the performance of standby counsel.
California decisions ... provide a narrow and limited range within which a [self-represented] defendant can raise the issue of ineffectiveness of advisory counsel. [...] Our recent decision in People v. Lawley (2002) 27 Cal.4th 102, 145 confirmed that when advisory counsel is appointed "the defendant is entitled to expect professionally competent assistance within the narrow scope of advisory counsel's proper role." We find no reason to reconsider that analysis.
Right to the "professionally competent" assistance of "advisory" or "standby" counsel
"[An appointed advisory] counsel [is] constitutionally [required to provide professionally competent assistance.]" (People v. Michaels, (2002) 28 Cal.4th 486, 515)
In light of the above: Although, in a criminal prosecution, courts may use discretion to appoint counsel for the assistance of a defendant who wants to assert his right to speak for themselves, to build their own strategy or execute defense through self-elected tactics, although rules in what case they may deny within their discretion are not clearly or distinctly enumerated or defined, such discretion may be abused, such abuse may be subject to review and reversal be warranted.
Some of them that may be surely ascertained by other decisional law or derived from other provisions of the Constitution:
(1) the defendant must be subjected to a criminal prosecution in a capital case;
(2) merely on affiliation, real or perceived, to any protected groups;
(3) if in a substantially similar case another was already afforded the assistance of counsel;
(4) if an adequate law library is not available to a pro se inmate;
(5) in complex cases reasonably foreseeably requiring the assistance of an adequate criminal lawyer;
(6) if the accused does not have access to adequate library for reasons outside of their control for e.g. libraries closed due to pandemic, homelessness; etc.
It will likely not be found to be an abuse of discretion by the court not to appoint counsel to assist the defendant if:
(1) an attorney, judge or prosecutor reasonably competent in criminal cases elects to not be represented, but be afforded the assistance of counsel; etc.
In between, it likely is truly a matter of discretion as things stand currently, but even the representative counsel construction of the counsel provision of the Sixth Amendment is not absolute necessitating appointment to for e.g. indigence.
Some other States that acknowledged a right to effective assistance of counsel while representing oneself in narrower or broader form
Supreme Court of Colorado
Downey v. People, 25 P.3d 1200 (Colo. 2001)
Supreme Court of Appeals of West Virginia:
State v. Layton, 189 W. Va. 470, 432 S.E.2d 740 (W. Va. 1993)
Some other states denying the right to effective assistance of counsel for defendants asserting charge of their case
Court of Appeals of the State of Idaho:
"[A defendant in a criminal prosecution] cannot waive [their] constitutional right to counsel and then claim a violation of that right." (Passons v. State, Docket No. 47124 (Idaho Ct. App. Dec. 18, 2020)
Court of Criminal Appeals of Tennessee at Nashville:
"The State is correct in its assertion that a defendant who represents himself cannot later bring a claim for ineffective assistance of his own counsel or for standby counsel appointed to assist him." (Ralph v. State, No. M2011-02067-CCA-R3-PC (Tenn. Crim. App. Dec. 20, 2012)
Further related laws:
"The fundamental constitutional right of access to the courts held to require prison authorities to assist inmates in the preparation and filing of meaningful legal papers by providing prisoners with adequate law libraries or adequate assistance from persons trained in the law" Bounds v. Smith, (1977) 430 U.S. 817