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I found a similar open issue regarding the filterable attribute in the Select component: [Bug Report] Select 组件的 filterable 属性在 1.3.5 版本后失效 ^[1]. This issue is still open and has no comments or references.

To resolve the issue where the Select component with the filterable attribute only displays one item after selection, ensure that the query is reset appropriately when a selection is made. The code should reset the query when values change, especially for multiple selections. Here's a relevant code snippet:

watch: {
    values ([value]) {
        if (!this.filterable) return;
        this.preventRemoteCall = true;
        if (this.multiple){
            this.query = '';
            this.preventRemoteCall = false; // this should be after the query change setter above
            return;
        }
        if (typeof value === 'undefined' || value === '' || value === null) this.query = '';
        else this.query = value.label;
        nextTick(() => this.preventRemoteCall = false); // this should be after the query change setter above
    },
    query (val) {
        if (this.preventRemoteCall) {
            this.preventRemoteCall = false;
            return;
        }
        this.$emit('on-query-change', val);
    },
    queryProp (query ){
        if (query !== this.query) this.query = query;
    },
}