Ty Cobb has put up the most career runs by a player against a team, with 342 runs versus the Yankees.

	NAME	R	OPP	G	AB	H	2B	3B	HR	RBI	BB	HBP	SO	SB	CS	PA	TB	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Ty Cobb T. Cobb	342	Yankees	443	1,660	619	117	53	23		176	11		103		1,884	911	193	37				.373	.436	.549	.985
2	Babe Ruth B. Ruth	338	Tigers	360	1,222	413	89	19	123	342	318	8	189	22		1,562	909	231	14				.338	.477	.744	1.221
3	Ty Cobb T. Cobb	323	Browns	429	1,597	568	96	45	26		190	13		135		1,854	832	167	54				.356	.428	.521	.949
4	Ty Cobb T. Cobb	319	Indians	432	1,654	580	105	34	15		160	14		135		1,858	798	154	35				.351		.482
5	Babe Ruth B. Ruth	318	Athletics	347	1,181	416	66	12	108	323	281	5	194	15		1,487	830	186	20				.352	.479	.703	1.181
6	Ty Cobb T. Cobb	316	Red Sox	437	1,657	615	97	53	13		175	17		139		1,891	857	163	42				.371	.436	.517	.954
7	Ty Cobb T. Cobb	316	Athletics	397	1,552	590	104	44	13		170	9		131		1,774	821	161	43				.380	.444	.529	.973
8	Babe Ruth B. Ruth	311	Browns	360	1,210	425	59	21	96	326	302	9	213	14		1,539	814	176	18				.351	.484	.673	1.157
9	Mel Ott M. Ott	304	Phillies	384	1,349	428	76	10	82	342	284	12	110	20		1,666	770	168	21			5	.317	.440	.571	1.011
10	Babe Ruth B. Ruth	303	White Sox	354	1,188	404	74	18	98	331	287	4	173	16		1,491	808	190	12				.340	.470	.680	1.150
11	Ty Cobb T. Cobb	302	Senators	434	1,592	605	97	38	16		194	13		145		1,841	826	151	42				.380	.451	.519	.970
12	Ty Cobb T. Cobb	301	White Sox	427	1,621	575	96	30	11		177	13		108		1,853	764	137	42				.355	.422	.471	.894
13	Stan Musial S. Musial	299	Dodgers	432	1,530	522	108	30	74	271	249	13	90	13	1	1,805	912	212	5	8	15	39	.341	.436	.596	1.032
14	Babe Ruth B. Ruth	298	Indians	361	1,143	405	69	17	92	278	348	6	176	12		1,510	784	178	13				.354	.507	.686	1.193
15	Stan Musial S. Musial	297	Phillies	417	1,547	522	116	35	54	261	197	8	110	12	4	1,765	870	205	8	5	13	30	.337	.414	.562	.976
16	Eddie Collins E. Collins	292	Tigers	405	1,430	499	69	24	5		242	11		125		1,760	631	98	77				.349	.447	.441	.888
17	Lou Gehrig L. Gehrig	291	Browns	310	1,138	404	75	23	92	305	250	8	95	13		1,410	801	190	14				.355	.474	.704	1.178
18	Paul Waner P. Waner	290	Phillies	356	1,369	469	97	25	30	223	182	3	47	7		1,582	706	152	28			2	.343	.421	.516	.937
19	Mel Ott M. Ott	287	Braves	368	1,252	389	72	12	73	232	250	10	107	18		1,522	704	157	10			5	.311	.429	.562	.992
20	Eddie Collins E. Collins	287	Browns	394	1,400	478	52	34	12		220	15		120		1,706	634	98	71				.341	.436	.453	.889
21	Tristram Speaker T. Speaker	286	Browns	392	1,448	519	100	32	21		196	15		65		1,698	746	153	39				.358	.440	.515	.955
22	Mel Ott M. Ott	285	Pirates	406	1,377	436	65	7	83	305	280	12	116	18		1,685	764	155	16			7	.317	.436	.555	.991
23	Babe Ruth B. Ruth	285	Red Sox	293	1,030	347	61	13	90	272	240	4	139	22		1,290	704	164	16				.337	.464	.683	1.147
24	Ted Williams T. Williams	284	Athletics	327	1,105	401	69	12	91	298	295	11	94	3	2	1,414	767	172	0	3	11	29	.363	.500	.694	1.194
25	Tristram Speaker T. Speaker	284	Yankees	410	1,517	499	120	24	27		185	13		66		1,762	748	171	47				.329	.406	.493	.899