Note that with the setup in the question where you first have style=apa, but later overwrite the citation style with citestyle=authoryear-comp you don't actually have APA style citations.
If you want real APA style, your document should probably look more like this
\documentclass{article}
\usepackage[
backend=biber,
style=apa,
apamaxprtauth=99,
]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{Biggs2008,
author = {Biggs, James and Marsh, Sarah and Johnson, Simon
and Walker, Steve and Grover, Bob and Girolami, Mark
and Mike, Sean},
journal = {Magic},
number = {5},
pages = {1--20},
title = {No1. paper},
volume = {4},
date = {2008-05},
}
@article{Bray2018,
author = {Bray, Yaya and Ferlay, George and Soerjomataram, Chris
and Simons, Rebecca L. and Torre, Ahmedin},
journal = {CA},
month = nov,
number = {6},
pages = {394--424},
title = {No2. paper},
volume = {68},
year = {2018},
}
@article{Larsen2013,
author = {Larsen, Max J. and Tan, Steve and Lænkholm, Martin
and Sørensen, Thomas V. O. and Ejlertsen, Mads},
journal = {PloS},
number = {5},
pages = {e64268},
title = {No3. paper},
volume = {8},
date = {2013-01},
}
@article{Larsen2014,
author = {Larsen, Max J. and Thomassen, Martin and Andersen, Kyle
and Kruse, Tim A. and James, Anne-Marie},
journal = {Medical},
number = {9},
title = {No4. paper},
volume = {7},
year = {2014},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
Some text \parencite{Bray2018}.
More text \parencite{Biggs2008},
and more \parencite{Larsen2013, Larsen2014}
Some text \parencite{Bray2018}.
More text \parencite{Biggs2008},
and more \parencite{Larsen2013, Larsen2014}
\printbibliography
\end{document}

Note how the first citation of each work uses the full author list (for up to six people), but subsequent citations use "et al.". Indeed \parencite{Larsen2013, Larsen2014} comes out as
(Larsen et al., 2013; Larsen et al., 2014)
from the second citation onwards.
If you want to stick to the mixture of style=apa, and citestyle=authoryear-comp, and want to get rid of the disambiguation feature, you'll need uniquelist=false. See Set limit to one author when using "et al." in biblatex.
\documentclass{article}
\usepackage[
backend=biber,
style=apa,
citestyle=authoryear-comp,
uniquelist=false,
labeldate=year,
apamaxprtauth=99,
]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{Biggs2008,
author = {Biggs, James and Marsh, Sarah and Johnson, Simon
and Walker, Steve and Grover, Bob and Girolami, Mark
and Mike, Sean},
journal = {Magic},
number = {5},
pages = {1--20},
title = {No1. paper},
volume = {4},
date = {2008-05},
}
@article{Bray2018,
author = {Bray, Yaya and Ferlay, George and Soerjomataram, Chris
and Simons, Rebecca L. and Torre, Ahmedin},
journal = {CA},
month = nov,
number = {6},
pages = {394--424},
title = {No2. paper},
volume = {68},
year = {2018},
}
@article{Larsen2013,
author = {Larsen, Max J. and Tan, Steve and Lænkholm, Martin
and Sørensen, Thomas V. O. and Ejlertsen, Mads},
journal = {PloS},
number = {5},
pages = {e64268},
title = {No3. paper},
volume = {8},
date = {2013-01},
}
@article{Larsen2014,
author = {Larsen, Max J. and Thomassen, Martin and Andersen, Kyle
and Kruse, Tim A. and James, Anne-Marie},
journal = {Medical},
number = {9},
title = {No4. paper},
volume = {7},
year = {2014},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
Some text \parencite{Bray2018}.
More text \parencite{Biggs2008},
and more \parencite{Larsen2013, Larsen2014}
Some text \parencite{Bray2018}.
More text \parencite{Biggs2008},
and more \parencite{Larsen2013, Larsen2014}
\printbibliography
\end{document}

Larsen 2013andLarsen 2014pieces each have but a single author? Or do you maybe want the citation call-outs to beLarsen et al. 2013andLarsen et al. 2014? – Mico Aug 01 '19 at 08:31Larsen et al., 2013, 2014orLarsen et al., 2013; Larsen et al., 2014is what I am after – George Aug 01 '19 at 08:46Author et al., 1990a; Author et al., 1990b. If that is used then the year in the bibliography would have to include the letter. I am open to other suggestions. I am okay with using the second author in citation in that instance alsoAuthour1, Author2 et al., 1990; Author1, Author3 et al., 1990. I don't think I'll come across a situation where the first two authors and year are identical (hopefully)! – George Aug 01 '19 at 10:00