NCCH2006/MK010 Trial (FORTUNE Trial)

Inclusion Criteria: 1. Participants with histologically or cytologically confirmed metastatic, unresectable, or recurrent solid tumor who agree to provide an archival tumor sample, a residual biopsy sample, or a fresh tumor biopsy sample 2. Ineffective to or intolerant to initial treatment, or for which standard treatment is no longer available 3. Participants with an FGFR gene alteration detected by NGS panel, who fall under one of the categories of groups A to C and E defined as below Group A: FGFR1-3 fusion Group B and E: FGFR1-3 specific activating mutations as below; FGFR1: P150S, T340M, R445W, N546K, K656E FGFR2: C62Y, A67V, N82K, D101Y, E160K, E163K, M186T, R203H, R210Q, Q212K, R251Q, S252W, P253R, P253L, A264T, W290C, K310R, Y328N, G364E, Y375C, C382R, A389T, V392A, R399Q, H416R, I422V, H544Q, N549H, N549K, N549D, N549S, L560F, K659E, K659N, R664W, E718K, S791T FGFR3: G380E, G380R, A391E, K650T, K650E, K650Q, K650N Group C: FGFR1-3 activating mutation not applicable to group B, or FGFR1, 2 gene amplification 4. For Group D, participants with cholangiocarcinoma who have previously received a selective FGFR inhibitor other than E7090 and have demonstrated progressive disease or resistance 5. Karnofsky Performance Status (KPS) \>= 70 for patients with primary CNS tumors. Performance Status (ECOG) 0-1 for patients with non-primary CNS tumors 6. For patients with non-primary CNS tumors, they have at least 1 lesion of \>= 10 millimeter (mm) in the longest diameter for a non-lymph node or \>= 15 mm in the short-axis diameter for a lymph node that is considered as serially measurable according to RECIST v1.1 using computerized tomography or magnetic resonance imaging (CT or MRI) within 28 days of enrollment. However, lesions that have received local treatment such as external-beam radiation therapy (EBRT) or radiofrequency ablation (RFA) must have progressed after these local treatment to count as measurable lesion 7. Participants with primary CNS tumors must meet all of the following criteria: 1. Have received prior treatment including radiation and/or chemotherapy, as recommended or appropriate for the CNS tumor type 2. Have \>= 1 site of bi-dimensionally measurable disease (confirmed by magnetic resonance imaging (MRI) and evaluable by RANO criteria), with the size of at least one of the measurable lesions \>= 1 cm in each dimension and noted on more than one imaging slice. Imaging study performed within 28 days before enrollment 3. Must be neurologically stable based on neurologic exam at least for the last 7 days prior to enrollment. (based on medical examination/interview) 8. Corrected calcium \<= 10.1 mg/dL 9. Phosphate \<= 4.6 mg/dL 10. Required treatment washout period, from the last day of prior treatment until enrollment of this trial, is as follows: 1. Antibody and other investigational drugs: \>= 28 days 2. Prior chemotherapy (excluding small-molecule targeted therapy), surgical therapy, radiation therapy: \>= 21 days (\>= 90 days from the date of the last radiation therapy for primary CNS tumors) 3. Endocrine therapy, immunotherapy, small-molecule targeted therapy: \>=14 days Exclusion Criteria: 1. Participants with brain, subdural or leptomeningeal metastases 2. Participants with primary CNS tumor located in either cerebellum, brainstem, spinal cord, pituitary gland, optic nerve or olfactory nerve 3. Positive for either human immunodeficiency virus (HIV) antibody, HBs antigen, or HCV antibody (patients with positive HCV antibody but no detectable HCV-RNA are not excluded) 4. Negative for HBs antigen, but positive for HBs antibody or HBc antibody, and also positive for HBV-DNA quantification (not excluded if HBV-DNA is below detection sensitivity) 5. Child-Pugh score B or C 6. Participants with pericardial effusion, pleural effusion, or ascites requiring treatment 7. Have any of the following ocular diseases 1. Grade 2 or higher corneal disorders 2. Active retinopathy (e.g., age-related macular degeneration, central serous chorioretinal disease, retinal tear) 8. Participants whose toxicity of previous treatment has not recovered to Grade 1 or lower per Common Terminology Criteria for Adverse Events (CTCAE v5.0), except for alopecia, infertility, and the laboratory test results listed in the inclusion criteria 9. Participants who received a prior selective FGFR inhibitor in the recurrent/metastatic disease setting; except for patients with cholangiocarcinoma harboring FGFR2 fusion (Group D). Note that prior use of a multi-kinase inhibitor which includes anti-FGFR activity is acceptable after review by the lead investigator 10. Participants who need the use of drugs that strongly inhibits or induces the metabolizing enzyme cytochrome P450 (CYP) 3A 11. The presence of FGFR gatekeeper mutations as follows: FGFR1 V561, FGFR2 V564/565, FGFR3 V555/557, FGFR4 V550 12. The presence of any of the following coexisting driver gene abnormalities: 1. Genetic mutations (excluding VUS): KRAS, NRAS, EGFR, or BRAF V600 2. Gene translocations: ALK, ROS1, or NTRK