<p>In this work, we investigate the mass spectra of all-charm (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(cc{\bar{c}}{\bar{c}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mi>c</mi> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> </math></EquationSource> </InlineEquation>) and doubly strange- doubly charm (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(ss{\bar{c}}{\bar{c}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mi>s</mi> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> </math></EquationSource> </InlineEquation>) tetraquark states using the framework of Regge phenomenology. Employing a quasi-linear Regge trajectory ansatz, we derive linear and quadratic mass inequalities for hadrons, which provide constraints on the masses of tetraquark states. We estimate the range of ground state masses of <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(cc{\bar{c}}{\bar{c}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mi>c</mi> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> </math></EquationSource> </InlineEquation> tetraquarks and determine the Regge slope parameters by fitting the corresponding <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\((J, M^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>J</mi> <mo>,</mo> <msup> <mi>M</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> trajectories. These parameters are then utilized to predict the mass spectra of orbital excited states of both <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(cc{\bar{c}}{\bar{c}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mi>c</mi> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(ss{\bar{c}}{\bar{c}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mi>s</mi> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mover accent="true"> <mrow> <mi>c</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> </math></EquationSource> </InlineEquation> systems in the <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\((J, M^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>J</mi> <mo>,</mo> <msup> <mi>M</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> plane. Furthermore, we extend our analysis to radial excitations by exploring Regge trajectories in the <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\((n, M^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <msup> <mi>M</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> plane. The obtained mass predictions are compared with existing theoretical results from various models. Additionally, we discuss the possible identification of the experimentally observed <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(\psi (4660)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mn>4660</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(\chi _{c0}(4700)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mn>4700</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> resonances as tetraquark candidates. The results presented in this study offer useful benchmarks for future experimental investigations and may assist in the spin-parity assignment of exotic hadronic states. Our findings contribute to a deeper understanding of multiquark dynamics and the spectroscopy of exotic hadrons within the framework of Quantum Chromodynamics.</p>