The Solubility of Tyrosine
According to Product  Information of Sigma-Aldrich for L-Tyrosine, the solubility is $\mathrm{pH}$-dependent:

Preparation Instructions: This product is soluble in $\pu{1 M} \ \ce{ HCl}$ ($\pu{100 mg/ml}$), with heating. The solubility in water ($\pu{25 ^\circ C}$) is $\pu{0.45 mg/ml}$ in the pH range $3.2-7.5$ (Ref.1). At $\mathrm{pH}$ $1.8$, the solubility is $\pu{2.0 mg/ml}$; at $\mathrm{pH}$ $9.5$, the solubility is $\pu{1.4 mg/ml}$; and at $\mathrm{pH}$ $10$, the solubility is $\pu{3.8 mg/ml}$.

The above claims can be justified by the study of the solubility of tyrosine in the acidic and basic conditions (Ref.2), the summery of which states that:

Measurements have been made of the solubility at $\pu{25 ^\circ C}$ of tyrosine in hydrochloric acid and in sodium hydroxide solutions varying from $0.001$ to $\pu{0.05 M}$, and also in distilled water. The $\mathrm{pH}$ of the saturated solutions was measured with the hydrogen electrode. The following values for the ionization constants of tyrosine have been obtained from the measurements: $k_\mathrm{b} = 1.57 \times 10^{–12}$, $k_\mathrm{a1} = 7.8 \times 10^{–10}$, $k_\mathrm{a2} = 8.5 \times 10^{–11}$. The changes in solubility with $\mathrm{pH}$ can be satisfactorily explained by the use of these ionization constants.

According to plot of solubility versus $\mathrm{pH}$ of their results, it was concluded that the highest solubility of tyrosine can be achieved in the $\mathrm{pH}$ range of $1-2$ or in the $\mathrm{pH}$ range of $9-10$. For example, the concentration of tyrosine in $\pu{0.05 M}$ $\ce{HCl}$ is found to be $\pu{0.0165 M}$ with the $\mathrm{pH}$ of solution being $1.450$. And also, the concentration of tyrosine in $\pu{0.0498 M}$ $\ce{NaOH}$ is found to be $\pu{0.0358 M}$ with the $\mathrm{pH}$ of solution being $9.953$. The least solubility of tyrosine is shown to be with in the $\mathrm{pH}$ range of $3-8.5$ (Ref.2).
Note: The extrapolation of the acidic side of above graph has shown the solubility increases up to about $\pu{0.04 M}$ at $\mathrm{pH} = 1$ (Ref.2).
References:

T. A. Brown, In Molecular Biology: LabFax; 1st Edition; Bios Scientific Publishers: Oxford, England, 1991, p. 29 (ISBN: 1‐872748‐00‐7).
David I. Hitchcock, &quot;The solubility of tyrosine in the acid and in alkali,&quot; Journal of General Physiology 1924, 6(6), 747–757 (https://doi.org/10.1085/jgp.6.6.747)(PDF).